I'd reseat and shoot them. Personally, I have no interest in removing and reseating
live primers, and I have no interest in removing my depriming pin from my sizing die to avoid depriming, and I have no interest in breaking down bullets, in general, so I reserve deconstruction only for those times when I have potentially dangerous or entirely unusable cartridges. I would seat deeper and shoot them.

My apologies for disagreeing with the community opinion, but I'm lazy.
WARNING: Seating bullets deeper after the cartridge is complete is NOT the same as, and should never be confused with, seating a PRIMER deeper after the cartridge has been completed. Primers do occasionally detonate during seating, and if you detonate a primer with a bullet and powder charge in the cartridge, that's going to be one extraordinarily bad day. Never reseat a primer on a completed cartridge.
You have another thing you might want to do here. Now that the push test has gotten you in the ball park for MAX OAL, you might want to consider getting an even more precise maximum. Sometimes the push test works out perfectly. Sometimes it misses by a hundredth or two. My CZ Shadow Line has a shorter than average throat, and my max with the Berry's FP is 1.069, so I would be a little suspicious that your 1.060 might be a hundredth or two off as a true MAX. Now that you have that ball park number, if you want an even more precise number, load a dummy round to 1.090, spin test it, looking for it to chamber completely and spin with zero drag. Then seat a little deeper, a little deeper, shortening it maybe .003 at a time, checking it each time, until it spins with zero drag. That will be your
true max. It might match your push test perfectly, or it might be a little longer. I had little doubt that the OAL you were giving us earlier that you were saying was fine was in fact way too long, but I suspect that 1.060 could be a little short, and this will give you a path to verifying the max OAL. Then knock .010-.015 off of that for a
working max.
As to your charges of Titegroup... The rule of thumb when you have multiple sources for load data is to go with the most conservative -- the lightest load window. In this case, despite multiple sources with some lighter than what you were planning on, I'd say you're fine at 4.0gr. The Hodgdon data for a short OAL lead bullet is 3.9gr - 4.3gr. Their data for 115gr plated GDHP is 4.5gr - 4.8gr, though at a little longer OAL. I simply wouldn't sweat 4.0gr as a starting load for that bullet, even without my own experience with Titegroup. And in my personal case, I have plenty of experience with Titegroup, and I load 3.9gr of TG with 125gr lead bullets and 4.1gr with 124gr JHP for 9mm minor competition loads, so 4.0gr of TG with a lighter plated bullet is nothing to worry about.
Again, get a more precise reading on your OAL max. It's great that you finally did the push test, but 1.06 might be little short, and there is something more you can do to get the number a little more precise.
Let us know.
Also, there is another stickie in this subforum titled "First Year Reloading: Issues and Insights" located here:
http://www.czfirearms.us/index.php?topic=59920.0It's not exactly a "how to" reload, but it's close enough that you would definitely learn some stuff from it if you haven't already read it. It's not the
end all of reloading, but there's quite a bit of some informative stuff in it.