Hello Ade,
Taylors were (traditionally) designed for 12s for the GC/x12 and GA/x14 bodies, whereas the old Jumbo/x15, dreadnaught/x10, and GS/x16 bodies were strung with 13s. The guitar top's bracing is designed for the tension of the 12s or 13s, so that is the factory's intent for tone and volume of each body shape. So a GA can accept 13s, and a GS can likewise accept 12s, all without issue to the structure of the guitar, but
your ears and hands can decide which gauge is best.
And as you noticed, the 11s on your 814 did not sound good to you, likely because the lighter 11s did not provide enough tension to "drive" the guitar's top so you probably perceived less bass and volume. You can try 13s on your GAs, and let
your ears determine whether the change is good, as well as whether you are ok with the increased tension for your fretting hand. Similar to you, I recently experimented going
down from the 13s to 12s on my dred because of nerve damage to my hand: I like the feel and the tone is good with the 12s. But I am now reconsidering going back to the 13s on this guitar as my health is improving and I miss the "bigger" sound of 13s.
One other side note with trying 13s: you "may" be able to get away with slightly lower string action. Depending on your playing style and how your guitar is set up now, the additional tension of medium-gauge strings may allow you to adjust your truss rod slightly (very slightly) for less "neck relief" which lowers your action a bit. It is subtle but can be a noticeable improvement. It is worth trying, and can always be put back to its former condition so there is no risk whatsoever.
May I also suggest Elixir's medium-lights where the EAD is from their medium set and the GBE from their lights. I use these Elixir PBs on GA and GC body Taylors and
love it. For me, I prefer the bigger bass notes and feel the tonal balance across all the strings is better than with a regular set of 12s.
Hope this gives you a few things to consider!

Edward