What kind of mixing ratio did he use when he sprayed the basecoat? The mix for BC is usually 1:1 color to reducer, where SS is often 8:1:1 color, reducer, and hardener. Basecoat isn't hardened, only the clear. For SS, the hardener also gives the finish a higher gloss and durability. Over or under-reducing can affect color match and coverage, more so with metallic/pearl colors.
See if the supplier will comp you a quart of clear and the appropriate hardener to fix the problem they created, or the SS setup you wanted in the first place. You can scuff the BC and then topcoat either way, either completing the BC/CC process, or topcoating with SS.
As far as paying for the labor, I think that's more on your painter for not verifying the paint and going ahead with the job than it is on the paint supplier. Did he do a sprayout card. or just open the can, mix it, and hit the quarter directly?
Generally, if we mis-mixed paint at my store, your only remedy was replacement paint.(And that was mostly for poor color match/wrong paint codes.) We also gave tech sheets to anyone who wasn't a "regular" or a body shop customer, indicating correct mixing ratio, spray pressures, etc.... for the kind of paint they purchased.
) I think I should just find someone who wants to take over the project. Really clean car!