We know that the ancient Greeks practiced gay sex not just casually, but even expectedly. The Romans did not.

Huh? The Romans were even more extreme with it. The Greeks would court young boys coming of age with a lengthy courting ritual that involved a lot of focus on consent - the Romans were straight up castrating prepubescent children to preserve their femininity.

In fact, it's probable that the "marriage is between a man and a woman" in the NT was an anachronistic reactionary response to gay marriage having become a legitimate Roman institution in the 60s CE following Nero marrying two men, first playing the role of the bride and then the role of the husband (the latter time with someone who had been castrated when prepubescent).

Even before the empire there were rules related to homosexual senators losing their voting rights if they were the bottom, and they weren't likely to create a rule for something that didn't happen.

So I'm not sure where you get the idea Rome didn't have homosexuality.

"Washing feet" was a actually a mistranslation of some kind of general "servicing" that had several meanings, including cock sucking or accepting being bottom.

I'd really need to see a source for this claim, as it sounds extremely spurious. There's a lot of literature around Christianity that claims secret coded language use, but generally they are all quite ridiculous claims.

While 'feet' or 'thigh' as words sometimes have euphemistic meaning for genitals, I'm unaware of any idiomatic use of "washing feet" as reference to sex. You can see some related discussion about the OT usage of a similar phrasing/theory here.