DI would take a bit of work and a high-pressure injection system. Remember, if it's DI, you're injecting into an already high pressure atmosphere while the cylinder is up.
You could set up a single cylinder EFI system that didn't inject fuel until (x)ms before the exhaust port was covered, thereby only letting fresh air flow out the exhaust. You've still got the oil issue, though, which I suppose can be made up for with synthetic/low E oils.
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