OP, it sounds to me like you have quite low self-esteem and are subconsciously projecting it onto your Scottish / Glaswegian heritage. In other words, I wonder if the root of the problem is more of an internal issue (your own explorations of sexuality, identity, self-confidence etc) but that you are masking these by effectively blaming where you come from.
Unfortunately, it is true that some people judge others by the way they speak, and there are prejudices particularly towards Northern accents (Teeside, Tyneside, Merseyside, Glaswegian etc). I think you can take some consolation from the fact that this issue affects a huge number of people, so you’re certainly not alone or in a unique situation. For people who do have strong, regional accents, it’s not about concealing them, but rather working positively with them. Some of the Scottish accents can be quite challenging for Southerners to fully comprehend (as can many other accents and dialects), so just make sure you speak slowly and avoid too much local slang when you talk with someone who isn’t local. There is no need to mask or apologise for your accent. Just try to keep it clear and accessible.
If you are unhappy in Scotland, then certainly it may be a great thing to relocate somewhere like London. But this will only work if you are secure and happy in yourself. If you have unresolved internal conflicts, they will simply go with you. I myself grew up near London, and I remember my parents wanted a clean break / new start in the West Country because they felt they didn’t fit in back home. They would often speak of how everything would be better once we moved to somewhere where we would be more comfortable. When we did eventually make the move, a lot of our problems came with us. It certainly wasn’t the dream escape it had been billed as. What I am saying is, it seems from what I’ve read as though you have issues with your own identity. Moving half way across the UK won’t necessarily fix that. What will fix it is learning to accept where you come from and accept who you are. You can’t change it, so you are going to have to take ownership of the fact you are indeed Scottish. Only once you’ve achieved that, will a fresh start offer the possible escape you’re seeking.
With regards losing the accent, you will find if you relocate that your accent will evolve. I used to have quite a posh Home Counties accent growing up, but it has become much less noticeable and decisively more Cornish since I moved here. I even find myself on occasion saying really Cornish phrases that have somehow seaped into my vocabulary. So you will soften your Glaswegian accent, but I think it’s unlikely you would ever truly lose it. And going back to my original point, why should you? Be proud of who you are.