So - every romulan couple has to have 3 children per 30 years:
If you take into account hazards such as pioneering, catastrophe, lack of resources, deaths, not finding mates, not having children, etc then every romulan couple has to have at least ~4 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.
In conclusion, 2 conditions are needed:
Romulans must breed like tribbles;
Romulans must hand-wave resources in order to support these next generations.
*In human history, couples could afford 5-6 children only because most didn't make it to adulthoold.
If we started with 10,000 people, and each couple in each generation produced an average of 3 children who in turn reproduced, the population of the Empire could be up to 110 billion people.
Now, I did stipulate three children surviving to reproduce another surviving three children. Not three children born.
This alone is a VERY high order.
This statement takes into account children and adults who don't survive to reproduce the average number. So, at that rate of population growth, you don't get "~1 - 10 billion," you get 110 billion people in the current population after two thousand years. This already takes into account illnesses, accidents, warfare and all other causes of "not reproducing the average number."
What losses due to illnesses, etc? What percentage?