Just throwing up some ideas here, not fully thought through so use as a basis for devising a system.
I understand the issue, and agree that a Li-ion battery is the most likely solution to being able to do the number of starts you need. The difference being that a Li-ion battery will accept charge at a vastly greater rate than a lead-acid so can recover very quickly.
Following on from some of the suggestions, I've been pondering whether a simple (relatively) dual battery system can be arranged.
Keep the lead-acid battery but don't use it for the starting current. Add a Li-ion battery which is used for starting.
Disconnect the cable to the starter solenoid from the lead-acid battery and fit it to the Li-ion +ve terminal. Connect the Li-ion +ve to the lead-acid +ve using a heavy duty "isolator" changeover relay (needs to be able to carry the max Li-ion charging rate, what do we guess, 40A fuse protected?). The link between batteries is "normally closed".
Take the starter signal wire from the starter solenoid and put it on the isolator relay coil. When energised by the ignition key going to crank position, it pulls the relay over to disconnect the link between the batteries, and a wire on the "normally-open" terminal then goes down to the starter solenoid to activate the starter. This means that the solenoid will only engage the starter motor once the 2 batteries are isolated and current comes from just the Li-ion one. Releasing the crank signal will de-energise the isolator relay and the batteries will be reconnected.
The big question is whether the Li-ion battery will be satisfactorily charged by the lead-acid based charging system.
A split charge relay unit might well be able to do the job for you, such as
https://brocott.co.uk/split-charge-relays/ , it would need a bit of investigation. I'm guessing it won't allow discharge from the second battery (the Li-ion, what would normally be the "leisure" battery in a caravan etc) back into the vehicle system, but may be wrong. It may be able to do all the charge regulation you need.
Just some ideas ......................