I've dealt with this quite a bit, good you got a meter, you can fish your hand between the pads of hay on the small squares, I got 25-30 off a load of 200 bales, years back that must have been a wet spot in the field and I spread out a tarp, placed the bales on it spread out, them cut the twine, fed it after some more dry time, did not lose any, but for horses we wait 2 weeks, while whatever happens as it dries or cures, some transition period where there is a concern about feeding fresh hay.
In the field, and its tricky with a belt kicker, we would loosen the bales a bit, then carefully handle and stack those so they would dry, did not lose many, but I don't care for loose bales, but... its the game you play sometimes to get it in. Changes from field to field, sometimes that darned windrow picks up moisture overnight, should have been flipped again, some fields not. Typically its tedded on morning of baling, then raked in the early afternoon and baled soon after, though with a bunch down, you can get ahead of yourself it windrows are left overnight.
I've done 2nd cut and played this game, down for days, tedded, raked and baled myself, and still had a borderline moisture issue, then as a favor to my father, knowing I had some really nice 2nd cut, I bought a bunch of it, and the problem in addition to the moisture, was our ability to store it, one barn too many roof leaks and the other, between watering the footing material, (riding arena) or just not enough ventilation, even with the doors open or what, on top of the stack I lost a bunch of this nice stuff, the regular hay guy even complimented it, we can grow some nice hay where I am 30 miles to the south. We lost a bunch of it, really ticked me off, well, frustrating, not only did I cut, ted, rake, stack behind the darned kicker with a man who would not drop a gear or two and help me a little, only so many wagons, the rest was baled in round, so I am getting nailed in the back of the head with bales, then transfer by hand to a tandem sileage body truck, haul 30 miles, and then toss em off to the help only to lose it to mold, it was borderline, now a hot dry barn would have been no issue with these bales, it would dry further if stacked right. I'm sort of done with bringing any quantity of hay there now, with all the variables, its just a losing proposition, and I never really minded doing it, even with all the work, well except getting hit off the head with those bales, more wagons, would have done it myself. Maybe at some future time, I do enjoy it, even with all the darned equipment and such, just not large scale or high pressure, have to have it, weather screws it up, oh well, there always next time, instead of you have to have it or your livestock will have no feed.
I have on occasion found hot bales, whatever you do, don't get complacent with this, I have seen the horrible results of that nearby, it is amazing at how hot these can get and with round bales, I've never experienced it, but know we have put up some with moisture that was questionable, always second cut in a field that has springs or wet areas ans this year those fields will not be drying out anytime soon.