First, in this application the thickness of the seal probably has no effect, as long as the position of the sealing lip is the same distance from the engine side of the seal (not the breaker points side). If that distance is not the same, the sealing lip may not run in the old position (the worn, polished circle around the shaft), which is not important anyway as long as the shaft is smooth, and the polished circle is not worn down to a smaller diameter. (Since the shaft is less than the seal's nominal diameter of 25 mm anyway, you would not want to make the situation worse by running the lip on a worn-down spot on the shaft.)
The picture of the ball races does not show the brand of the new one. Because it is marked 6205/P6, I think it is probably SKF brand, because P6 is a specific SKF tolerance class. The old bearing was NTN brand. They are both reputable brands, and they are both 6205 open bearings. The minor variations in features between manufacturers are not something to be concerned about. The important thing is whether the old one has any more slack in it than the new one. If you can reduce the slack (amount the outer ring can move radially or axially when you hold the inner ring in a fixed position) by replacing the bearing, that will make life easier for the oil seal.
The first important test is whether the main lip of the oil seal contacts the shaft securely all the way around it. The second important test is whether it does so when shaft, bearing and seal are all installed in the engine. Aside from that, and making sure the seal is installed the correct way around, without any trauma to the seal's lip during assembly, it should work. Note that it is desirable to lubricate the seal lip before you push the shaft through it.
Please post some pictures as you go along with the assembly process. I still don't have any clue as to why the seals leaked on your previous tries at assembling the engine. There is still some mystery here, and it has the capacity to bite us on the backside.
