Hooking up my compressor to my dryer outlet
Given the proximity of the 10-30R receptacle to the panel, and the presence of conduit connecting the two, you could upgrade the 10-30R to a 14-30R and likewise swap out the power cord on the dryer. That's something like US$25 in parts. This is an upgrade that is just good sense to implement.
If you upgrade to a 14-30R then you could easily make or buy an adapter from the 14-30P to L6-30R. It would deal with the ground-vs-neutral situation correctly.
There's also another option. Since the panel is just right there, get a bit of conduit and a box and install a new L6-30R receptacle. I believe code allows multiple 30A receptacles to be fed from a 30A breaker. If the panel has no room for a new breaker and you don't want to replace existing breakers with a quad breaker solution, you could choose to feed both receptacles from the one existing breaker. The terminal on your breaker might be designed for landing two conductors, but if not, attach a pigtail of wire to the breaker and use a wire nut to join the pigtail with the leads going to the two receptacles (times two: this same arrangement for both poles of the breaker).
The two-receptacles-one-breaker arrangement could be accomplished by putting the junction in the box with the dryer outlet but it might violate box fill rules and definitely would be crowded and hard to work with. It'll be much easier to run the conductors from a new receptacle directly into the breaker box and make the junction there.