I think you should hold your ground too. (At least until they give logic a chance(!)) I've been on Lamictal for years and adjusting dosages (various levels between 200 and 400) has been a key strategy. Wouldn't have been if it hadn't have worked. So <raises hand> it's worked for me too.
Not saying it's been the
only strategy, but it is the first one. Always. If/when that doesn't work,
then another med will be added or adjusted. And, you know, we went with something that had already proven
helpful in the past(!)
I know 200 mg is called "therapeutic dose", but it seems rather dogmatic to see that so literally and rigidly. I wonder if that is reflected in solid (and current) research or if it's simply the thing that got stuck in people's heads at one point then not really thought about subsequently. TOTALLY a pondering, but it might be worth looking into.
I'd push on the low risk angle for sure. What HARM is there in TRYING a dosage increase? As a starting point. That is all you are asking. It is perfectly reasonable. It's not like you're ruling out looking at other options if that doesn't work. You are NOWHERE NEAR a ceiling effective dosage. (Generally considered to be 400mg) It's a med you have not had trouble with. That's important. It's a very logical place to start (as you already know of course).
Maybe you can throw in, "humor me". (Who knows, they might even learn something to do so(!)

)