A campaign might lack the technical ability to figure out which CD a voter is registered in, however a courthouse can do it fairly easily.
If it is just a matter of 500 signatures in each CD, that’s one thing; now yes, the courthouse must determine whether the signatures are valid. Typically they do not check every signature, but take a sample and estimate.
One rub is that some (all?) of the states are using new CD lines. SC elected 2 delegates from each of its 7 new CDs - there are 6 in the current Congress.
I’m sure there is software to geocode addresses (I’m not sure if the campaigns type in ballot signature addresses at the end of the day) although getting the CD lines to check against is a technical challenge, maybe especially so for an underfinanced campaign.
It sure gets complicated, but it’s a shame if he can’t be in the race over 30 disqualified signatures.