check for burrs on the rim at the stem hole and sand or file them down, if you haven't already.
I have, however, I don't see how it might matter in my case.
With the new tube only about half of the Presta stem is sticking out of the rim. Another half is actually inside the rim. It is not possible to pull the stem out any further. Apparently, the rigid valve base is wedged between the sides of the rim, which prevents it from seating fully against the inner surface of the rim. This means that the actual base of the valve remains pretty far from the hole. Whatever irregularities I might have around the hole, they can't really come in contact with the tube.