Yes, a bad fuel injector could be the issue. Certainly worth a closer inspection.
I know there is a thread (or more) where someone else had this issue with the injector causing the misfire.
There are coolant lines around the oil filter for cooling. Those aren't that tough to replace while the coolant system is drained.
The other thing I'd look are where the coolant hoses mate to the aluminum thermostat housing inlet and the by-pass pipe, is for pitting in the aluminum. Make sure...
How is the status of the rest of your coolant system? Radiator cap and thermostat (with gasket) are cheap insurance. What about the heater T's?
Make sure you flush the system out very well, to insure all the residual green coolant is out. @2001LC has great threads about coolant system maintenance.
I have a brand new set sitting in the closet in my office (bought them in the fall from Impex). I will look at them today and see what they have on them.
Sounds like a brake booster system failing as @StevenH mentioned.
If you are on any of the 100 Series Facebook Groups, there is a member Andy Lee who specializes in rebuilding them. He's got a good reputation and it fairly quick if memory serves.
That is very interesting. Anti-seize added?
I have been checking torque on my plugs for the last 2-3 years every 6-12 months. I've never found them to be out of spec. Torque has been 17-18ft-lbs
I agree with @SteveH. Take it on a good drive
It is strange how some vehicles react to being disconnected from the battery. I know in my case, mine may run rough for a minute, but it levels out fairly quick. My old 80 Series took a little longer to smooth out.
Decided it was time for a spot check on my plugs. All good @18ft-lbs and had driven ~6600 miles since I previous checked them in September 2022. Before that I had checked them August 2021 and had driven 6700 miles.
If nothing else, it is peace of mind.
Check your torque!
This looks like it will be a good time for all involved!
Need to get a few projects done on my LX before any road trips, but hope to catch one the Indiana LC events in 2024!
You may have better luck in one of the 100 Series Facebook groups. I know there are a few UK based Land Cruiser groups which might help you narrow/refine your search.
Try here as well - The Toyota Landcruiser Owners Club :: Index - https://www.tlocuk.co.uk/forums/