My at-home strategy had two stages:
- Reveal 6 cars in "anchor" positions: corners (1-3, 13-15) and sides (7-9)
- Reveal a new number and usually call out its match from the six anchors. Lather, rinse, repeat.
Most good players can easily remember 6 cars in these specific locations. There are possible hurdles (matching in stage 1; revealing two cars that didn't match any anchor in stage 2) but these are at most a temporary setback.
While I know what you mean, I'm very amused by the fact that matching can be considered a setback.