OK. It's done. Turned into a complete debacle.
Plan A was the angle grinder but it was incredibly difficult to get just the paint off without making the joints look terrible. So, I scrapped that and went to plan B. Plan B was an assortment of wire wheels on the drill. That worked pretty well to remove the top coat of paint but did not get down enough to get the bottom coat of paint. So, it was on to Plan C: paint stripper.
Paint stripper and a steel brush worked extremely well. However, removing the stripper/paint residue goo was a nightmare. I had ground the floor last weekend and I think the resulting texture is what made it made it extremely difficult to remove the residue. I went through a gallon of Xylene and every curse word I know and there was still residue.
Before I started the joints on Saturday the floor was otherwise completely ready to go. By the time I gave up on scrubbing I now had water beading on the area around the joints. Maybe more scrubbing would have worked but after all the prep already invested I was not going to leave anything to chance. So, I rented the Diamabrush on Sunday (again) and reground the floor.
So, word of advice to anyone else getting ready to do there floor with a similar issue, learn from my mistake and: remove the paint from the joints before you grind the floor!
Needless to say, I am glad it's over.