As to their combat power, I have put them through several balance passes with a couple volunteer beta testers over the course of the mod and I feel they are in a good space right now. In my games I role play as a scavenger and do not buy ships so I only use the ones I start off with and salvage. I have not done a full "JYD only" fleet game in some time though I set up the faction to offer every class and type of ship so maybe I'll do that. I'm working on a Hiver update ATM but once that is done, I'll do a balance pass on them again, nothing too drastic mind you I don't want you to fall out of love!
I am just playing a Nex campaign as pirates with this as the only faction mod added, neither I nor the AI has much of a chance against the JYD. I replaced my regular tankers with JYD tankers (and not the combat tanker), they have more capacity and all other stats are better, they also come with drones and thus can be deployed in combat, in contrast to my regular tankers. The troop transport is even worse, has advanced grounds support package and enough points that I can use it safely as a missile boat in combat.
Meanwhile I rip through Hegemony, Luddic Church, Tri Tachyon, etc. fleets like butter [EDIT2: with my regular fleet]. Might be wrong, but to me it seems like every JYD ship has like 20-60 extra OP points available in comparison to vanilla, on top of that a good flux ratio and almost always built in drones / fighters etc.
EDIT: great work and I really appreciate it, yet I don't think the ships are balanced or I am doing something completely wrong. I generally try to play only with pirate ships, I have a few captured JYD ships in my line-up, but they just feel too strong also when I use them.