There are a variety of sludge / varnish remover products out there, e.g. SeaFoam in the oil, etc. I think any of them would help, and be a prudent course of action. I have used them to clean up various engines, and they all work, at least to some degree. My advice would be use one of them, run the engine hard for ten hours or so, change the oil and filter, add some more detergent / or Tuffoil, and do some accelerated oil changes for awhile.
It isn't my money, but having owned a number of engines with hydraulic lifters, I would change the hydraulic lifters. It is tough to get them clean without disassembly, and not all versions disassemble easily. They need oil to operate, and they really should not go in and out with finger pressure. I suspect that having forced the oil out of the lifter, where it was doing its job, you now have some air inside, allowing the motion with finger pressure. I think of the concept of a hydraulic lifter as using engine oil to expand the lifter to just the right height, keeping the valve clearance at the optimal height. If they are super springy, they won't keep the height up. (They need pressure to overcome the resistance of the valve springs after all.)
I think from the damage that your engine,
@Modrob, has apparently had, there was probably a loss of lubrication, probably due to fuel in the oil, and you are working through the after effects.
I think that the good news is what you have found is all readily fixable.
All the best,
Peter
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