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Personally, I would never dream of scheduling a flight so close to hot-range activity, though I know some individuals have to do so by apparent necessity. As the OP's account details, it is all too easy for something to go wrong, and if you do not have some sort of official status (like being a sworn LEO, or a congresscritter---a CHL does not count), then trouble will accummulate quickly.

In times past I have typically worn a completely different change of clothes for flying, one that was not worn at the range, so as to minimize the chances of any stray cartridges or other gun paraphernalia being left behind in a pocket, or burnt powder residue (possibly?) setting off the puffing sensor machines (not sure what exactly to call those). Easy in and out, come and go. Take some time and use a little forethought to make TSA's job as easy as possible, and you just "get on down the road," to paraphrase Rick Perry.