Music Man Majesty tuning issues

I’ve had my Majesty for a while now and absolutely love everything about it except one thing…tuning stability. I will start off saying I don’t have much experience with tremelo systems. These issues started occuring before I even used the tremelo bar. Ok, when I first noticed this issue, I contacted customer support and explained the issue and they responded with “we recommend Big Bends Nut Sauce in the nut and bridge.” So, I ordered some and applied it on my next string change. It definitely helped some, but the problem still persists. If I use the tremelo bar, even moderately, it goes out of tune even worse. My Majesty came with RPS 10’s and that’s all I’ve ever used when restringing…exact same size and brand. My bridge is flush with the guitar and perfectly parallel. When I restring, I line the tuner hole up with the incoming string and pull the string through snug, then tighten the locking tuner, tune the string and cut off the excess string. When I’m done tuning, the string doesn’t even have a full wrap around the tuner, which seems to be the universal opinion on how to do it correctly. Like I said before, I don’t have a lot of experience with tremelos, but I did have a couple of questions:
1) When stretching the strings on a floating system, do you guys block the trem? I did and the reason I ask is because if its not blocked, when you stretch the strings the tremelo will slightly move freely, which seems like the string stetching won’t get 100% of the benefit of being stretched. I did a lot of reading (trying to educate myself on this issue), but didn’t see many people saying they blocked the trem while string stretching.

2) When you notice your guitar out of tune is there a particular order to tuning? Some people say low E string first, then high E next, then A string, etc. Other people say tune the string thats off most first and the that usually helps bring everything else together. Lots of different opinions on tuning order, so I really wonder if it matters.

Sorry this post is rather long. I just wanted to share my issue and how I’m going about trying to narrow down the solution. I do really love this guitar, but this tuning problem has really bummed me out. Since its still under warranty, Ernie Ball has also offered to look at this issue themselves, but then I would have to ship the guitar across country and be without a guitar for probably a couple of weeks. The very thought of not having a guitar that long would completely stress me out, so that would be an absolute last option. I am taking the guitar to a local luthier this weekend and see if he can fix it. I’ve read lots of posts and articles on this issue, but just can’t figure it out. Even though I’m taking it to a luthier, I would still appreciate any input you guys may have. A sincere thanks!