You're tightening it down too tight on the cones. Too much pressure against the bearings, when you tighten the axle, stiffens it up too much.

On wheels I've worked with. On each side of the axle there are two nuts. The inner nut is closer to the wheel, and another nut outside of that tightens against the inner nut. How much you tighten down the inner nut is the key.

Then you put the wheel in the fork and tighten that down, it makes it slightly tighter.

You have to hold the inner nut in place with a wrench while tightening the outer nut with another wrench. On both sides. The outer nut is only there to hold the inner one tight. They have to be tight against each other. But you don't want the inner nut too tight against the wheel. Since your adjustment changed, you didn't have the nuts tight enough against each other.

With the wheel by itself off the bike, you want the axle to feel just a little loose. You can feel just a little bit of play if you spin the wheel while holding the axle. Don't worry about that play or looseness, because it will be tighter when you put it on the bike.

So here's how you get there. You want to first get it where there is no play, and then adjust it to where there's a little play. First get all the nuts loose, then screw the inner nuts down against the hub. Tighten the outer nuts to finger tight. Now on one side, using two wrenches, tighten the two nuts against each other pretty tight. Spin the wheel. If you feel any play, the axle wobbling, tighten down the inner nut on the loose side (the side where you didn't tighten the nuts against each other), just a fraction of a turn. Keep doing that again until the wheel spins without any play. Now, just back it off a small bit, part of a turn. Do that until you feel a little looseness in the axle. At that point, using two wrenches and holding the inner nut solid, tighten the outer nut against the inner one, tight. Then you should be set.