Save yourself a headache: remove the ballasts and rewire the fixtures to directly power LED bulbs designed to work without a ballast.
I had exactly the same problem: I had a mixture of old-style and newfangled electronic ballasts and it was a total crapshoot whether a bulb that worked in one would work in the other. Mostly not on both the one and the other and those that did work would randomly just stop working.
The "compatible ballasts" lists that the manufacturers provide are not only mostly wishful thinking, but you have to take the fixture apart to find the ballast model number anyway.
Bypassing the ballast involves clipping a couple of wires to/from the ballast and hooking them up to eachother without the ballast in the way.
The wiring diagram for removing the ballast is included in the package or is directly on the sleeve for the direct-wire LED bulbs. There are only two wires coming into the fixture in the first place; one goes to one end, the other to the other. Rocket science it ain't.
You've been meaning to clean them up anyway; might as well rewire them too! Putting them back up without the ballasts is way easier, too; those old ones are heavy!
Please take the ballasts to be properly recycled! The old ones are full of incredibly nasty stuff; the older the nastier. The electronic ones can have lead solder depending on when and where they were made. Think of it this way: if you throw them in the trash, they will come back to haunt you through your faucet.