C-6
I do not know the LAA maintanence schedules, as I live in a different country and we might have different rules here. However, these are my observations.

Regarding the overhaul of the engine. I would have thought that as the aircraft (and engine) is on a permit to fly, you would be allowed to do the overhaul yourself under the supervision of an inspector. That is at least how it works here out in the sticks. An overhaul to serviceable limits is just about getting the book out and measuring components, looking for corrosion etc. As you are already an aircraft engineer (albeit without CAA endorsment), I think you should not find this too complicated. Hey, even I did an overhaul on a Continental A-65 a few years ago under the watchful eye of my inspector! If the UK rules are different, I appologize for the red herring 😉

Regarding the engine in the aircraft you are thinking about buying. I think you should not worry too much, the Continental is a tough little engine. It does have weaknesses, but they are GENERALLY less expensive than the known weaknesses on a Lycoming. When you inspect the aircraft (assuming you have not done so already), you have to look for oil leaks. Typical weak spot the crank shaft seal at the front of the engine and the O-rings in the valve train. Nothing expensive and (relatively) easily rectified.
The engine as you describe it has only run about one third of it´s live, the recommanded TBO for the small Continentals typically being 1800 hours. When you inspect the aircraft check if the aircraft has been flown regulary. If it has not, you can expect to have to do a top overhaul on the engine soon-ish. It might be ok for a year, or maybe longer, but on the Continental USUALLY the first item to go after a long time of inactiveness are the cylender (or rather the piston rings) giving you zero compression. If you are lucky, you might be able to salvage the rings and hone the cylenders but you should give a thought about replacing them all when the first one fails as the other ones will probably fail shortly.
You have a few possibilities to renew the cylenders. You could find old jugs and pistons that are within serviceable limits and buy a new ring kits for them.
If you feel posh, you could by a complete new cylender assembly (jug, piston rings etc.) and be set back about 1000 dollars for each jug.
If you are operating on a shoe string, take the old ones (all of them when the first one fails), and salvage what you can and by new rings for the rest.
If I was in your shoes, I would go with option one. As soon as you buy the aircraft, get the overhaul manual for the engine. Start looking for Jugs and pistons that are within serviceable limits. When it starts going pear shaped, by new rings for and exchange all at once. As a permit to fly aircraft and engine I THINK you can do all the work yourself with an inspector looking over your shoulder.

When you inspect the aircraft, find someone familiar with the type. If such a guy is not available, go for someone that knows similar aircraft types or the type of construction. Have him/her look the aircraft over to see if there is something obviously wrong. He/she might not be able to find everything that is wrong, but it would at least give you an idea of whether or not you are buying a turkey or an aeroplane.