I've been reading through the Cambridge History of the Native Peoples of the Americas, and in the Gulf Coast chapter, it's repeatedly stressed that the Gulf Coast is not as well studied as most of Mesoamerica, and the Postclassic period is especially little-known.
Similarly, Smith and Berdan's The Postclassic Mesoamerican World has chapters for virtually every region of Mesoamerica, from Jalisco to Belize... except for the Gulf Coast.
Finally, a brief search on Google Books yields no specific monographs on Postclassic Totonac archaeology, one anthology on the Postclassic Huastecs, and nothing on the Postclassic Olmecapan.
Why is this?
You are correct that the Postclassic Gulf Coast is not very well understood. The two principal reasons for this is that the Gulf Coast is generally an understudied region in Mesoamerica and the fact that population was lower in the Postclassic Gulf Coast than in previous periods and had a much more dispersed settlement pattern (Gattray and Stark 2002). These two factors together give us little information to work with. Fewer people means fewer material remains to study, and when people aren't looking at a region that much it makes it much harder to find information about it. There has been some research in the area, notably by Barbara Stark, that gives us insights into what was going on there in the Postclassic. I'll first provide a brief summary of what we do know about Postclassic Veracruz before discussing the factors that make studying this period difficult.
What We Know
First, for context, the Gulf Coast was the seat of a large complex civilization in the Classic (AD 200-600) period that had a population density comparable to that of their contemporaries, the Classic Maya. Unlike the Maya, however, they built earthen pyramids rather and clay sculptures since workable stone is rare in that region. Their monumental architecture was still stunningly large, however. Typically, Classic Period civic-ceremonial cores were arranged around a "standard plan" which had a large pyramid and a ball court on opposite sides of a large plaza with two parallel linear structures on the other two sides (Stark 2016). Stark (2016) argues these linear structures were likely council halls that represented a corporate governmental authority, perhaps a representative body of different lineage heads, or something equivalent. These cities supported themselves through an intensive agricultural system using gridded canal networks that drained retained water in the dry season and drained water during the rainy season. The Classic Gulf Coast had extensive trade with Teotihuacan, and developed large cities, but was not likely ever unified into a single state. Stark (2016) argues that while large regional capitals like Cerro de las Mesas did emerge during the Classic Period, the apparent uniformity of plaza layouts appears to represent a shared cultural tradition rather than a top-down imposition of imperial authority.
The Classic Period Veracruz culture declined and was reorganized following the collapse of Teotihuacan around AD 550. During the Epiclassic (AD 600 - 900) a new major city emerged in the northern foothills, El Tajin. El Tajin appropriated many of the cultural symbols of the earlier Classic Period Veracruz culture, such as heavy use of Venus (the planet) imagery, but also presents new innovations on the earlier Classic Period centers. Most notably, unlike the Classic Period cities El Tajin's monumental architecture was made from stone and is made of a style that is totally unique. El Tajin declines in the Early Postclassic, and in the Middle Postclassic there was major disjuncture associated with the Totonac migrations.
The Totonacs were the dominant ethnic group on the Gulf Coast at the time of contact, however, they were relatively recent migrants to the region who immigrated into the region near the beginning of the Middle Postclassic Period (AD 1250 or so). Where they came from exactly is a bit of a mystery (Evans 2004), as is whether they intermarried with or displaced whatever original ethnic group inhabited the Gulf Coast. We can see their migration not just through ethnohistory, but archaeologically. The Middle Postclassic period (AD 1250-1350) marks a major disjuncture in material culture from earlier periods (Curet et al 1994). Sites during this period are much more dispersed than in previous periods, but they also conform to a more "concentric" settlement layout where elites are concentrated near the civic-ceremonial core and commoners are more distant (Gattray and Stark 2002). There is strong evidence of trade and interaction with highland Mexican cultures at this time including the importation of foreign ceramics and participation in the broader "Mixteca-Puebla" (aka "Postclassic International") art style (Gattray and Stark 2002; Curet et al 1994). Ceramics made in this style appear in the Gulf Coast at the same time that previous ceramic styles disappear, marking a total disjuncture from earlier cultural patterns (Gattray and Stark 2002). Curet and colleagues (1994) actually argue that a particularly large and unusually dense Middle Postclassic settlement, El Sauce, may have been founded by an invading polity from the highlands.
The Late Postclassic Period (AD 1350 - 1521) marks the period of Aztec imperialism in the region. However, the Aztec Empire's conquests and subsequent control over the region was not uniform. The Totonacs did not have particularly large cities compared to the earlier Classic Period culture, and what cities they had were fairly dispersed in layout. Some of these cities, like Cempola, Cotaxtla, and Tlacotalpan appear to have become Aztec tributary provinces. Others, like Tlalixcoyan, remained independent but sandwiched between Aztec territories (Garraty and Stark 2004). One of the results of this imperialism was that economic inequality in Totonac society increased (Garraty and Stark 2004), as the elites who collaborated with the Aztecs profited, while the overall wealth of commoners decreased.
Why We Don't Know More
To get back to your original question, this adds to the problem with studying the Postclassic on the Gulf Coast, as impoverished households have less "things" for archaeologists to study. Their architecture is typically of poorer construction, which means it doesn't preserve as well. They typically have fewer decorated ceramic vessels, and opt for plain brown ware utilitarian vessels that aren't diagnostic of any time period or culture in particular. When you add to this the fact that Postclassic cities are typically located underneath modern cities, as well as the points I mentioned above that Postclassic settlements were less densely populated and the region is understudied in general, you can begin to understand why this is kind of a blank space on the chronological map. Gattray and Stark (2004) spend a good chunk of the introduction to their article lamenting the lack of published ceramic and settlement data on the Postclassic in Veracruz. Often times, Postclassic artifacts are only found as sparse deposits overlaying far more substantial Classic Period deposits. Because there's not much to work with, scholars will frequently publish articles about the material they have, and simply ignore the Postclassic artifacts because they don't have a large enough sample to say anything meaningful. This isn't to say there hasn't been research on the period, but to understand this period scholars are forced to compare sparse collections from multiple field projects, which is a tedious and time-consuming process that up until recent years hadn't really been done. This is a shame, because Postclassic Veracruz is a really interesting period for studying migrations and cultural disjuncture. Research in the region is still ongoing though, and maybe in a few more decades we'll know more.