Hmm... that's some good feedback. Generally, I tried to make hyperspace remnants as similar to vanilla remnants as possible, which is the reason they're limited in the ways you mentioned. It's certainly possible for me to change that, and I think I will.
"allowHyperspaceRemnantsToUseEmergencyBurn":false,
"allowHyperspaceRemnantsToUseSustainedBurn":false,
E-burn is very powerful and remnants are faster than average anyway, so I don't think I'll allow them to use it by default until I've had a chance to playtest it. I don't like the idea of hyperspace remnants behaving differently than normal remnants in the same game, so I'll make these settings apply universally unless there's sufficient demand for splitting them.
"allowHyperspaceRemnantsToJump":true,
If remnants occupy hyperspace, it makes sense that they should be able to move between hyperspace and normal space. I worry that allowing normal remnants to jump might cause unexpected problems, so I'll probably only allow hyperspace remnant fleets to do so.
I might be able to do something about them giving up the chase too easily as well, although in my experience they mostly tend to do this when it becomes obvious that they can't catch me anyway.