It seems that one of the great differences between the modern world and any earlier period is communication. Specifically, the lack of it in the past.

This is a faulty premise, unfortunately.

languages still seem to have evolved more or less consistently wishin (within?) geographic boundaries.

It's precisely because of communication that the geographic boundaries are so well represented in linguistic diversity. The verbal (non-written) communication continued as far as it was geographically easy, and then stopped. This is why you find again and again that things like mountain ranges and large rivers form clean lines between dialect groups.

This actually leads to some interesting situations when things like river courses change. In the past, the Yangtze River was the clear line of demarcation between Wu dialects and Mandarin dialects. However at some point in the past the course of the river shifted, so that a village which was once to the south of the river is now today to its north. Their speech still represents it's southern roots, but now instead of being surrounded by other dialects of its own group, its a linguistic island in a Mandarin speaking area.

While the comment that people may live and die within 5 miles (or whatever) of each other may hold true, people still very much interacted with the people around them to the extent that it was convenient or necessary. You do find much greater linguistic diversity in mountainous areas, in many cases at least, because communication was more difficult so people did tend to not interact as much or be influenced as easily, but in lowland areas you see a much broader extent of linguistic contact and co-evolution.

Admittedly, one English villager from the 16th century would likely have trouble understanding another from a village several miles away,

A more likely scenario is that they'd speak different but still understand each other just fine. There's a high incidence of learned intelligibility among neighbouring groups. That is, maybe I don't understand your language if I just hear it, but it's close enough I can learn to understand it quite easily compared to, like, Arabic (for us as English speakers). This has historically been a common occurrence. You speak X and I speak Y but I can understand you and you can understand me so still we communicate, and if this happened over a prolonged period of time in a stable environment, we see convergence between X and Y, even if X and Y are not closely related.

and certainly dialects were more prominent then than after radio, television, and widespread literacy.

This is actually not true. Even the internet hasn't really slowed down the momentum of dialect divergence. Yeah, you're reading the same thing that I'm typing, but I'm not typing it too representative of my dialect, and you're probably reading it in your own accent anyway. Maybe I'm going out of my way (whether I know it or not) to not use things that I know would make it harder for you to understand since I assume you're not part of my dialect group. I'm accommodating to you in how I'm writing this.

Even so, coevolution of languages still seems to exist. I just can't quite figure out how.

Basically, divergence happens all the time, and convergence happens all the time, and both are operating under different pressures to different degrees at different times. Communication has been more widespread than your question presupposes, and things like print media have done little to stop divergence.

The one thing it has done to encourage convergence is promote borrowings. I think your culture is pretty rad, and you guys have all these great words. We have words for those things too, but yours sound so modern and cosmopolitan, so we start to borrow them. This happened with Old Korean where you see the Silla borrowing extensively from Chinese when other Korean kingdoms of the time were not (or were not to the extent that Silla was). Eventually Silla's dialect becomes Middle Korean so now Modern Korean has a bunch of Chinese words. But this was intentional borrowing, and not something that was fated to happen.