If you are having balance issues on the 12'6 x 28", which is a very stable platform for your dimensions, then you might need to get some more time on the water and paddle it in choppy/tricky conditions to get used to it. I am your age but a bit lighter (85kg) and a lot shorter and have no issues on my Fanatic 12'6 x 27.5". I SUP surf a lot on small boards (8'5 and 7'4) so that helps with balance. I've tried a load of different race boards and they are all pretty good for stability and even the narrow board sub-25" still have good secondary stability to recover from a wobble. If you want to get into down winders you need to have fairly stable board but more importantly know how to read the bumps and surf them. I do some social racing and get my arse kicked but as soon as it gets choppy or we go on a proper downwinder a lot of the guys who are fast in flat water start falling off

as they struggle with the lumpy stuff which is good for me as I purposely paddle in choppy waters to get a good feel for the board and then use my balance and experience reading the water state.
Paddle length and technique is important too.
See if you can demo some boards if at all possible.