After reading of your dramas with your engine and quick look through the replies, I'd have to say that your engine has definitely not had a proper recondition as such and looks to me as quick slap together to sell a car, or as we use to call them: car yard rebuild. There are a few things I've seen, most of which I'd say have been pointed out, but not seeing it in person and only seeing in pictures can look heaps different. As for what to do, I'm not really sure as I don't know of your budget on getting your car running again. The simplest and easiest way might be, get a good pair of used cylinder heads, where the valves seat proud (yours are sunk too far and look at the "burn" mark on that ex valve) and don't leak (fill ports with kero and leave overnight) or have you heads reconditioned with new valves and inserts on the exhaust side. Another possibility is maybe using a 4V exhaust valve as it may machine out enough for the valve to seat proud. If the intakes are looking iffy, use a valve that's 2.08-2.1 in diameter, don't use a 4V intake valve (can be done) as they're really too big on a 2V head.
Realistically, I personally think the engine should be gone right through and everything measured and checked, but as I said, I don't know your budget or what you're willing to spend on getting it running again. If the engine was fine besides the loss in compression (looks like head gasket blown between 2 cylinders in the pic, but hard to tell without being there) then maybe go with what I stated above about the heads and see if that'll get you out of trouble.
On the exhaust inserts, I don't know what the dramas are about running them. Personally I have inserted hundreds maybe even a thousand plus heads without dramas, everything from daily drivers to full on race engines with none falling out or even springing a leak from slightly hitting a water jacket. I just use to give the insert .005-.008in crush, freeze the insert, a bit of loctite, press or "drive" in the insert then pressure test for atleast an hour at 60-75 psi. No pinning of the insert, nothing extra at all and never had a problem with any of them.
Anyway best of luck with it and hope it all works for you and doesn't become too costly for you. As has been said, what one person considers rebuilt is another persons slap together, unfortunately.