Disagree with this not being feasible for a local region. San Diego region had a successful system for this where you registered your regional competition number annually (with a fee to have your Solo Card and ownership of that number). The SCCA magazine (which we should all be receiving with our memberships) has advertisements in the back for multiple vendors supplying numbers that fill this need.
If people are spending $1000/year on tires, it's not a huge ask to improve the running of the event to have somebody spend $60 on numbers. Roll the annual number registration in with annual tech. For newer entrants, temporary 4 digit numbers were assigned and the paper + painters tape method was required. Eventually, they decide that they want to "look the part" at the events and buy numbers as well. This seems to come up every few years, and I haven't understood the pushback to improvement, other than just being resistant to change.