The lug nuts seem to be deep enough

Nah, the top end of those lug nuts will pop off before restriction.

You may could find a bushing to go into each of the bolt holes before the lug nut. But I would just replace the studs with the thicker option that matches the wheel hole bore. Buy a few of the "Lisle Wheel Stud Installer" tools locally or from Amazon, and you can do it without a press.