Help: Music Man John Petrucci JP6 Noob Questions and Concerns

I just bought a 2015 Music Man John Petrucci JP6 in Mystic Dream, which is the guitar of my dreams. It was new, but had spent a few years in the guitar shop, and unsurprisingly been played a lot by the customers of the store.

I’m a complete beginner to tremolo systems; nevertheless, I tried to set it up and change the strings myself, that took a while, but I could get it there eventually.

The tuning stability is fantastic, even with aggressive dive bombs. However, since this is my first time with a floating tremolo bridge guitar ever, I have some questions/concerns:

The guitar goes out of tune if I hold it facing towards the ceiling or the floor. It comes back in tune when it is sitting in playing position on my lap. Is this behaviour normal for floating tremolo bridges? I did not notice any problem with the bridge itself. Note that I’m using a 9-46 gauge string set as opposed to the 10-46 set that would come with the guitar from the factory.

One more thing that concerns me a bit, is a slight misalignment of the neck with respect to the body. It’s actually not a misalignment, as the neck is sitting very flush to the body. It’s just that at the heel joint there is a bit of wood on the neck that should also sit flush with the body, but it does not. I looked at the angle of the strings with respect to the neck, and they are pretty straight looking to me. So it means that the neck is correctly positioned, and perhaps only unfortunately this neck wasn’t the best fit for this particular body. Also, there is a small gap on one side of the neck joint to the body. Probably this is just an aesthetic thing. Please see the images below.

Thank you in advance for your help.