I worry about it too, Naproxen helps me a bit, but try to avoid when I can. I haven't had any upset stomach problems so far
Naproxen helps me significantly, including staving off full-blown iritis if I take a couple at the first warning signs of eye irritation!
Unfortunately I overdid it; after taking one (or sometimes two) Aleve everyday for 1.5 years, heartburn started coming on

Whoops, so much for that advice from a doc that one Aleve a day was such a small amount, don't need to worry about digestive issues... luckily the heartburn cleared up quickly once I switched from Aleve to NSD for my standard anti-inflammation strategy.
Still, I keep a bottle of Aleve around for occasional use, and have had to use it quash eye irritation when my diet experiments went awry. I recall you're prone to that stupid iritis as well, so definitely keep that in mind if your eyes ever start to feel irritated.