Because the jump ship has to pass through itself there is no "park it on this side and other ships go back and forth."  Standard transit is just a game short cut for the sake of player convenience.  It saves you having to split up your forces for squadron transits and to re-transit the jump ship between each ferry job, it also removes the scatter and the time you need to get the tender back to the jump point.

In a squadron transit: the jump ship also transits.   

What is actually happening when you use "standard transit" and the tender can't jump all the ships in the group is that the jump ship forms a squadron with some ships.  Then those ships jump through, the jump ship jumps back and forms a new squadron with the remaining ships and that new squadron jumps through and then the tender jumps back.  You should only use standard transit on jump points where no threat can exist and where the saved time is not of any real significance.   

A tender with a jump engine that can't jump itself can't work...or better put, should not work.

Your results make no sense.  You have a 45kt jump tender, with a 5.4 kt mil jump engine, it can't jump a 5.4 kt ship as it can't jump itself.   So your first config 1 should never work as the engine's jump capacity is below the size of the ship mounting it.

Config 2 (45kt mil jump engine) should work, and it does unsurprisingly.

Config 1 (5.4 kt mil jump engine and 45 kt commercial) can't work for the same reasons that a 5.4 kt military jump engine doesn't work (jump engine smaller than ship mounting it)--that this doesn't work while the other did is very odd.

Config 2 (45 kt mil jump enine and 45 kt commercial) is pointless as a 45kt military jump engine can jump a comercial engined ship through anyway.  But regardless there is no obvious reason why this doesn't work.

Commercial jump engines can jump commercial drive ships only.  Military jump engines can jump either commercial engine or military engine ships through so long as the jumping ship's mass is below the jump drive limit (smaller of mounting ship size or drive rating).

This may just be a question of if Steve programed the check to look for 2 jump drives and only he can reply to that.   I would suggest using a jump tender with a single jump drive as that most assuredly works, even if you need two tender classes.

Once you updated the design, did you open the ship in the ship viewer?  This forces the software to load the new design instead of the old design staying in the buffers.

Exactly 45k. The original version was at efficiency 6, now I am at 10 so I was moving from 50 HS only to 90 HS. I removed like one layer of armor and one CIWS so I could fit that SMed 45k military jump drive.

And you still had that other Military Drive on the design? Because I know THAT causes some problems.

I have just tried this. I have used SM, unlocked the Gatebuilder and replaced the 15k military jump drive with 45k one. Limeleaf was still unable to jump.

What was the final size of the Gatebuilder? 15k to 45k jump drive is a fairly big increase. If the new size of the Gatebuilder is over 45k, you are still stuck.

Your military JD cannot work, AFAIK, because your ship is bigger, than her military JD max ship size.

It just doesn't work? Even when trying to tender for small enough military ships?

I have just tried this. I have used SM, unlocked the Gatebuilder and replaced the 15k military jump drive with 45k one. Limeleaf was still unable to jump.

Your military JD cannot work, AFAIK, because your ship is bigger, than her military JD max ship size.

That hidden Jump Drive may be the cause of your issue as my similar builds work and show both drives. Try jumping the carrier by itself with the Gatekeeper just sitting on the point (each in different groups), they are supposed to be able to do that (they did in previous versions at least). Your issue may be the Gatekeeper not being able to jump because it is thinking its only capable of 15k tons limit for jumping (because what you described is that the Gatekeeper and the carrier are in the same group, which makes the game think the group is all military, which makes it only want to use the military drive).