Maybe a different option: get a small diesel (Kubota or Perkins) and adapt to a manual tranny. Industrial motors don't have all the plastic bits that modern car engines have and will visually fit better with the antique car. A lightweight car would still allow for brisk acceleration with the relatively low power output. Aero will still be awful, but the inherent efficiency of the diesel may help make up for it.
Want to improve aero? Maybe look at the Modified Roadster classes from land speed racing (/FMR /GMR /BFMR /BGMR) for ideas.
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