I did the same thing when I mounted my upper shock mounts. I normally don't use fine thread, but when I started thinking about it, I might have gotten only one or two coarse threads in 3/16. It made sense to go with fine instead. I was still a little leery, but I got 3-4 good threads in there I think, so it should be ok...I built mine the same way and have not had any problems. You did bring out one important point that many are not aware of and that is to tap all holes with fine thread, very important.
Jim