I'm not sure how far along you are. Have you/he basically "ruled out" chronic TTTS at this point?
How has your diet been, and your weight gain? (In terms of # of pounds gained by 20 weeks gestation, 28 weeks gestation, etc.) You probably know that an early weight gain and a diet high in protein & complex carbohydrates (lots of vegetables) improve your odds as far as chronic TTTS, low birthweight, preterm labor and "typical" twin complications. I suspect that the same things, and a good iron level, are protective against acute TTTS, as well. But as stated, there isn't a lot of research or information available about acute TTTS....in terms of what precipitates it, what might protect against it, and what the meaningful statistics are.
I've seen recommendations for delivery via c-section at or by 37 weeks, but 34 weeks? True that there's a chance of acute TTTS developing at and after that time of gestation, but the risks of c-section not to mention the risk of pre-term and near-term issues are much better documented and statistically significant.
Your doctor makes his recommendation based on the hope that he can completely rule out one scary risk, but YOU are the one who will endure the crucible of the NICU experience, not him.
I went through this whole process of decision-making recently (my mono-di boy twins were born on July 20) and it was agonizing. My doctor was recommending an induction after 38 weeks. I felt the safest thing, in terms of acute TTTS, would be a c-section (albeit I would not have considered it at 34 weeks, or at 36 weeks!) but I was not convinced that the risk of acute TTTS justified the risk of elective c-section.
Once I realized that the only thing I really feared was acute TTTS, and I had no real control over that (other than my health, nutrition, etc.), I wasn't comfortable consenting to an induction. (The reasoning for the induction wasn't really the acute TTTS risk, it was more the idea that "twins are 'term' earlier" and that the placental function would diminish with gestational age and complications go up.)
I have a stack of printed articles (obtained online and also through Interlibrary Loan) on subjects like near-term issues with elective delivery of TERM fetuses, are twins "term" early, what is the "ideal" gestational age for delivery of mono-di twins, etc. etc. I read all of those things during my pregnancy and over time, they informed my decision-making pretty solidly.
It still was a difficult process because there is no way to know for sure what will happen. I did become (reasonably) comfortable with the decision to forego elective c-section to lessen risk of acute TTTS, with the acceptance that you only know it would have been the "right thing" after the worst thing happened. That was a part of being informed, for me...realizing that, but still believing that the risk of acute TTTS did not seem to justify the risks of elective c-section.
Who knows....c-section may be right for you, but the window your doctor is suggesting seems REALLY precipitous and I don't know if that could be right.
Good luck to you.