Is it a case of just gaining Hrs elsewhere
Yes and lot's of them.
and then paying for an endorsement?
No. If someone wants you to fly their jet around, they should and will pay for your endorsement.
There are a few jobs around where you can get an F/O spot with very few hours, but in 99% of cases you'll be the F/O forever. If however, you get into corporate with several thousand hours broken down into lot's of hours in different area's (night, turbine, command, multi engine) then you'll have a much better chance of progressing further than that co-pilot seat into a wider range of aircraft.
Think of it like this. In that part of the industry, you need to make yourself attractive with your extensive experience so that those who want the best, will want you. They can have whoever they want because it's a highly sought after and small part of the industry, so you're better off giving yourself the absolute best chance and get the experience first.
I've got just on 4,000hrs, nearly 1,000 night command and about 2,000 turbine command and I'd still consider myself not even anywhere near what people like that would want, unless I want to end up the Captain's bitch for the rest of my career.
morno