You are right that tube size does not matter for braze-on FD.
Are you set on having only Ultegra parts? There's plenty other cranksets out thereof similar quality that would give you more chances of finding 165mm cranks. A chain-ring swap won't help as the chain-rings mount on the crank, so you'll still be looking for a 165mm crank.
Yes, a 10 speed cassette will fit on your 8 speed hub. You'll need a spacer behind the largest cog, but they're cheap and easy to come by.
If money is tight, you could just get cassette, chain and compact crank and you will be able to run 10 speed.