Is there a way to overdrive a single phase, capacitor start, AC motor?
It appears that you have found one of the very few VFDs on the market that are designed for single-phase motors. It is likely that that the V/f ratio has sufficient adjustment range to do what you want without a transformer. Transformers are difficult to deal with on the output of the VFD because the V/f ratio at start and very low frequencies may need to be significantly higher than the rated V/f. Try to download the manual and check the adjustment range of the V/f.

The VFD that you selected may be manufactured by someone other than the seller. If the seller will not let you download the manual before buying, try to determine if it is available from the manufacturer.