Testing with the hammer and trigger not installed is the same as testing it uncocked. Assembling those parts won't help fix the leak.The things that could leak on the closing stroke like you described are the middle seal between the valve body and exhaust body, the seal between the nut and exhaust body, and the exhaust poppet's sealing surface against the exhaust body. If tightening the retaining bolt doesn't help, you'll need to disassemble and verify all sealing surfaces are clean and none were damaged during assembly. You may also want to verify that the original lead seal between the valve body and exhaust body is not still in the valve- if it is, you may wish to leave it there and try to reassemble without that seal from your kit, or remove it and assemble with only that seal from your kit.Aso verify that when you assembled it, the small valve spring went in first, then the separating washer, then the longer, stiffer spring with its big end toward the front of the gun. If these springs are reversed it might not have enough pressure to hold the exhaust valve closed. The longest skinniest spring is the hammer spring. I hope that made sense...Good luck!
Yes there needs to be a seal under the nut. The factory one is lead and forms around the nut in a conical shape- the flat side of the nut points toward the back of the gun.
I used Mac1 white PTFE seals front and back. They were thinner and took up less space making them easier to start the nut. They have been in the gun several years now and never lose air even stored away with 2 pumps . I never could get the lead one to reseal well.
As mentioned before Tim McMurray at Mac1 Airguns is an expert on these that many have used to rebuild if you go that route. You might try making sure all seal surfaces are clean and the intake button type seal is in the tube correctly, not upside down flipped when dropped in the tube. I would then try to form a seal to replace the lead or that thick white seal with one made from TEF Valve Packing Rope from Lowes. It can be formed into a softer O ring and used in place of one of your current seals. That will have more room to compress and tighten down. I did this on a 312 Benjamin, which has a similar seal, for a quick fix that has worked for 5 years now. You could also try the thin PTFE valve seals from Mac1 in his parts listing if you want to keep working on it. Thats my best advice for a home fix. This is the rope seal stuff that I used on the 312. That white O ring in your picture does look very thick and may be hard to get compressed.
Get the seals from Tim, as mentioned above, and you'll have no problem sealing it. Much cheaper than sending the gun to him for repair, and you'll have the satisfaction of doing it yourself. Those aftermarket lead seals are too "dang" hard to compress, that's why you're having trouble.
Only suggestion I have is to check inside the tube one more time to make sure there is not another lead seal still seated where the white o ring will seat on, based on the inability to get things to thread as they should leads me to believe there is something there giving just enough thickness to prevent threading the nut.