Probably crazy to mention given all you said you've done, but what about the thermostat? Without a thermostat in place, or with the thermostat stuck wide open, many engines will have enough flow going through the radiator to cause water to come out if the cap is off. Even if it's just stuck wide open the lack of restriction in the system will allow the water to flow too fast and not release enough ehat into the radiator and that alone will cause one to heat. So, if you haven't checked or changed it already I'd definately try that.
Anothetr thing to check on the older machines is the pressure regulator on the radiator. Look just to one side of the fill port for a round disc with several bolts in it. If you take it off there should be a spring, a disc, and another thin plate that acts as a seat under it. Make sure that everything is clean and free to move, that the disc and sealing surface are clean, etc, etc. Too make sure the sealing disc on the main radiator cap is good too so it seals. Without these items in place and working properly the radiator will not build any pressure internally, and, like a standard radiator without a pressure cap, it will not cool like it's supposed to.
I read your post below and the seal rings on the liners will allow coolant into the oil, but they have nothing to do with any kind of compression/ pressure getting into the cooling system. In other words the o-rings on the liners shouldn't be an issue unless you start seeing coolant in your oil.
Sounds like you've done and checked alot of stuff already, but those are a few things I would check first if called out to a customers machine, hope they help.