I think GitLab is a reaction to the problems GitHub has, to me it IS the response to the letter, though maybe not the one you'd first expect!
74 karma · joined November 11, 2015
What's great about GitLab, there's a release on the 22nd of each month, so you can depend on pretty much continual improvement. Even if you don't think GitLab is suitable for your Open Source project, talk to the team on their issue tracker, things get solved pretty quickly!
This is speculation, unless you have inside information, UXKit could well be under active development - we don't know.
For Trident, Private/Private repos work the same - though for GitHub in particular you must have a paid account for Private repos.
There will be an update very soon to fix this.
Self Hosted GitLab connections should be fine.