Don't sell yourself short on how much being a dispatcher will add to your resume. I'd stay at your current employer, get current, and should have no issues getting interviews at any major.

Something that I haven't seen mentioned is... Theres something to be said about showing loyalty to an airline as well as upward career progression, I would say it generally would look good on paper in future interviews if you stay at the current ULCC and become a pilot there. If nothing else it would be a positive talking point in an interview.

I'll add a counterpoint regarding your training history; Completing initial new hire training with no further issues at a new airline would show future employers that the training failure is in the past and not something to worry about.