A couple of observations: (1) In most non-industrial societies meat is a luxury, so it wouldn't be too hard to just not eat any meat. Pythagoreans might still have a problem, because of the apparent injunction against beans, but Torah doesn't say anything about plants that I can think of. (2) Most of what we currently think of as Jewish Law, particularly the well-known and complex things like food and Sabbath law, saw a lot of their development after the first century CE, and particularly in late antiquity and the middle ages. Those conversations were definitely happening in the Hellenistic and early Roman periods, but the major rabbinic writings tend to come after the Bar Kochba revolt in the second century.

In the Second Temple period (which "year 0" falls near the end of), the big question was about "gentile food," and there were differing opinions. This seems to be the period in which the pig begins to surpass other unclean animals as the quintessential non-kosher animal, because pigs are relatively cheap to farm and therefore more common near among lower classes. So it makes a convenient cultural boundary, which is the point. Galatians 2:11-14 documents that some Jews were uncomfortable with eating with gentiles at all, regardless of the menu. Daniel 1:8 and Tobit 1:10-13 both express disgust at eating food prepared by gentiles, without specifying the type of food or whether gentiles might be present while eating. All of these passages are vague and in the context of agenda-setting, but they document that at least some of the very pious were going beyond what Torah requires on it's own. Here it's worth remembering that you rarely use something as an example of piety unless there are others who aren't doing it--the characters Daniel and Tobit being all high and mighty about not eating gentile food implies the existence of Jews who didn't care or at least cared less. (A good academic book on this topic is by David C. Kraemer).

So what if you're especially pious and live in or travel to Rome? Probably your best option for food that hasn't been contaminated by gentiles or gentile utensils is to stay in Jewish neighborhoods. There were Jewish communities in most major cities around the empire, and a large one in Rome, and it would be natural for someone traveling from Judea (or from another city's Jewish community) to stay with relatives/friends or present themselves at the synagogue in a new city and find hospitality from there. That way they'd get all their food from Jews, and as long as they found someone equally pious they'd be fine. For someone keeping Torah but not worried about general contamination by gentiles, staying vegetarian would usually be enough.