Agree, I wouldn't want less than 2 mm of protrusion with horizontal dropouts especially. For most rear sprockets of 13 or 14 teeth, you need 3-4 mm of clearance between the outer face of the smallest sprocket and the locknut face. Maybe less for 12 teeth and definitely more for 15 teeth, neither common on freewheels now.
Yes if you put an extra washer under the right locknut to get this clearance, you will be better to re-centre the rim, particularly if you move one from the left side to the right side, and this will make the wheel more off-centre with respect to the hub when you're done. Not everyone would re-centre for a small change like this, but I would, and do, just because otherwise it's not as good as I can make it. If you can get by with only a 0.5 mm washer, so much the better. That might be all it takes. There will be a lot of trial and error, and much adjusting of cones on both sides. You will be taking the freewheel off to adjust the right axle stack, then putting it back on (just till it seats) to check clearance. Repeat until OK.
You say the chain only "sometimes" jams when shifting from smallest to next larger. What happens is that as the derailer first pushes inward to derail the chain, it (the chain) momentarily tilts outward on the cog tooth so the upper outer edge of the outer link plate is now sweeping out a space wider than the chain was when it was running on the smallest sprocket. The chain returns to vertical as it moves inward and gets out of the way. With the jam being a sometimes thing, you might be just a hair's-breadth short of adequate clearance -- enough to clear the inner link edges but not enough to clear all the outer link edges all the time. If the chain is by chance catching on the dropout itself, you can try filing a little relief just where that link plate edge goes by. It might take only a few file strokes. I have a bike with high dropouts where that worked. But alas in your situation I wouldn't file the stay itself, being thin. Is this a frame with vertical dropouts?
But the bottom line is, if you have 4 mm of axle showing now, you can probably fix the problem with 1 mm or less of movement, so you should be fine all around. The filing idea is just if you're that close to clear and have a nice thick dropout to file. Saves having to attack the axle stacks and re-centre the rim.
Last edited by conspiratemus1; 08-14-19 at 11:56 AM.