If you take 0,02 rate of growth per year, then every romulan couple has to have 3 VERY SPECIAL children per 30 years:
Every single one of these children must survive and each have 3 children.
If you take into account hazards such as pioneering, catastrophe, lack of resources, deaths, not finding mates, not having 3 children, etc then every romulan couple has to have at least ~5 children per 30 years (a few "spares").
Which raises the problem: how does a colony manage to feed/educate/etc a population 3 times as numerous as the preceding one, every 30 years?*
Not by building ships and going somewhere where there's no infrastructure.
And not by having magic tech (as Kirk's childhood colony - and every other failed colony in trek) proves.
Oops. Looks like there's no beating that petri-dish.
They don't have to be like bacteria to have a massive population. You do know that a sextillion is, say, a million times more than a quadrillion right? They could be the most unfortunate species in the galaxy, suffer all the catastrophies possible, and could easily reach the quadrillion range. In fact, the more they spread out on other planets, the less impact any kind of catastrophy would have on them. And you keep bringing up human history, like the Romulans are going to suffer from bad teeth, influenza, no food, stroke and heart attacks due to obesity, chicken pox, scarlet fever, mumps, malaria, amscesses, and other 20th century diseases that can be prevented in a society that uses science.
Your estimates of 40k are laughable.