Do the math, man. Read 705.12 and/or what's been written above.
120% of busbar minus the main breaker is what you have left for the solar plus.
With a 200A panel and 200A main breaker:
(1.2*200)-200= 40A left for solar, not enough for you
225 panel with 200A main breaker:
(1.2*225)-200= 70A left for solar, enough for you
200A panel with 175A breaker:
(1.2*200)-175= 65A left, also works.
Seriously consider this option. Almost no dwelling in my experience really needs 200A, especially one that was living on 100A. Are you really adding more than 75A of calculated load?
Or just redo the tap. Whatever's easier and cheaper for you.
(BTW, it's very unlikely the panel would actually be overloaded, but the code is conservative.)