Is there any way to use oversized okra?
In my experience (I'm Texan, I've seen my share of okra), 2.5-3" is pretty small, and 6" is on the big side but I wouldn't expect it to be inedible. It's certainly going to be much more tender at 2.5-3"; there's no possible way it'll be too tough to eat. Larger does mean tougher, but at that size they might still be okay (for example this source says 4-6" is good). It looks like different varieties can have pretty different sizes - for example, this cow's horn okra is supposed to be best at 6-7" but still be good at 14"!

In any case, test the okra you have; no reason to choose just based on the length. Just try cutting it with a sharp knife, and if it's really hard and fibrous, you'll know. If it's borderline, any sort of long stewing method will be your best bet. You'd also want to cut it fairly thinly, so that you don't have very long fibrous strands to try to chew.

If it's really too hard to soften even like that, you might still be able to get some use out of it as a thickener but I don't think you'll ever be eating it on its own. If you want to try thickening with it, I'd cut it into bigger chunks, so that you can easily fish them out once they've done their work.