What a mess! This is, basically, a smuggling operation. The intervening space between Coventry and Thorin belongs, ostensibly, to KSD and the Loyalists at this point who will surely capture or destroy any unescorted ships in service to the Allies.
No, that's not correct. Space is big, BT's ships have comparatively short sensor ranges. The arrival pulses are hard to mask, but after that it's easy to disappear in a star system and recharge before defenders can get to you. Just scoot somewhere around the proximity limit away from the zenith/nadir points, recharge, and jump. However, you did point out the less stressful option:
each jump will have to be to either uninhabited or abandoned systems, for recharging stops,
Yep. There are a lot of unoccupied systems in the Inner Sphere - about 1000 systems per inhabited one. You don't need to worry about using systems held by Katrina loyalists if you don't want to.
With adequate timing, each time a Merchant-class arrives in Coventry system, three DropShips are already waiting at the jump point, or will be there by the time the JumpShip is ready to depart.
A Merchant carries 2 DropShips. It's the Invaders that haul 3. Or did you mean the JumpShips sacrificed a docking collar for the LF battery and are flying together as a squadron of 3 ships?
Down to the basics of the journey, assuming a command circuit with 1 ship hauling 2 DropShips:
1) You've got (approximately) a week of transit from jump point to planet at each end. This has been addressed by "three DropShips are already waiting at the jump point, or will be there by the time the JumpShip is ready to depart." That works.
2) 320 light-years is 11 jumps no matter how you cut it. You've got 3 KF-equipped JumpShips lined up in (I assume) a command circuit for the task, and together they can make 6 jumps before needing to recharge, which will take about a week. Assuming that they have plentiful fuel handy, they can recharge both KF core and LF battery simultaneously (with sail and fusion reactor) in about a week, actually a bit less without risking core damage.
So the timing looks like:
--Start. Freshly charged LF JumpShip #1 has 2 or 3 DropShips dock to it in Coventry. Day 0.
--Jump 1, Jump 2. Day 0.
--Handoff: DropShips transfer to JumpShip #2. Day 0.
--Jump 3, Jump 4. Day 0.
--Handoff: DropShips transfer to JumpShip #3. Day 0.
--Jump 5, Jump 6. Day 0.
--Recharge begins for JumpShip #3, about 6-7 days.
--Jump 7, Jump 8, Day 7.
--Recharge begins for JumpShip #3, about 6-7 days.
--Jump 9, Jump 10, Day 14.
--Recharge begins for JumpShip #3, about 6-7 days.
--Jump 11, arrival in Thorin with one unused Jump, Day 21.
--DropShips fly from jump point to Thorin, about 7 days (without looking up Thorin's transit time), arriving Day 28.
--The return trip would be about as long.
There are two options to cut down transit time:
1) Use more JumpShips. A chain of 11 JumpShips, no LF batteries, will be able to deliver the DropShips from Coventry to Thorin in 1 day. The slowest part of the sequence will be jump point-to-planet flight, and the next slowest will be the ~7 days of recharge for the entire command circuit. Assuming two or three squadrons of DropShips circulating at each end of the circuit, you can make the entire command circuit flush one JumpShip's load of DropShips through the command circuit each week.
2) Try quick charging. For modest target numbers, each LF JumpShip should be able to cut recharge times down to 5 days. Those 3 recharge periods will be completed in two weeks (15 days), allowing a Coventry-to-Thorin flight of 4 weeks (one week for DropShips to fly from Coventry to jump point, two weeks for the JumpShips to make the 11 jumps in a partial command circuit, and one week to go from the jump point to Thorin).
*********************
Now, if I misunderstood and the LF ships are flying as a squadron, this whole process gets longer. The squadron can only make 2 jumps per recharge period. You've got 11 jumps. That's 5 recharges and 25 days, or 20 days if you gamble more with quick charging. That gets you down to 3 weeks, not counting DropShip flights.
But a command circuit with 11 conventional JumpShips could be faster still.