I've asked what you do to keep a JAR licence current. The answer was 'That's your own business..." So are you able to line-up a trainer & simulator to do an LPC without too much hassle (I'm UK based by the way).
Do you have the 757/767 on your JAR licence? If you do then there's no need for anything like an instructor for an LPC. At licence renewal time you get a CAA Class 1 medical done and submit your logbook, which shows you are current on type on an aircraft on your JAR licence. Don't know how you go about getting the 757/767 on your JAR licence if you don't already but talk to FCL and they'll tell you. The LPC-type sim checks appear in your logbook, so the CAA can see you are current.
What is the cost of accommodation in Japan? Given that AJX do not pay for accommodation costs unless you're on a trip and that you're not there half the time, is it practical or affordable to rent a flat / studio / room?
Excel Hotel is JPY5775 per night. You are given an accomm allowance or $550/month (with additions for exchange rate literally just being introduced for Jan onwards). Pax guys spend more time in the hotel than cargo. A lot of the pax guys rent apartments between 2/3 of them. Some of the cargo guys do but fewer than the pax lot. It will take up all of your accomm allowance and then a bit more but some guys are willing to pay for the freedom it affords. Others prefer the hotel to do their laundry
Horses for courses but it can and is done.