Rod rigging is great if you need its advantages of weight aloft, wind resistance, etc. But for cruising it's not necessary and its failures can be pretty spectacular. I would say if it passes survey by a qualified rigger, keep it. But if there is ANY question in ANY part of the turnbuckles, tangs, etc., go with one-size-up SS wire rigging and new fittings. It's a once-every-10 years cost, but if you are going from Florida to the Black Sea, which side of the equation do you want to be on? You can move to Norseman/Sta-Lok or equivalent terminals, which will allow you to make up a spare stay if needed aboard.
Just my opinion. I have what looks to be perfectly good 1988 5/16" SS wire stays on my steel cutter (only been in fresh water), but I will change them all before we go cruising for new stays, because 20 year old wire might make excellent spares, but I'm not going to test it against the ocean.