Moving the engine midship isn't the greatest way to cure snap oversteer. It will just add some nasty understeer before the weight-related oversteer occurs.
If you're getting snap, that's all down to the suspension and tires. A stiffer front bar or a softer rear bar... change the alignment... change the tires...
If you really want to do the mid-engined thing, you'll still have to fix the suspension, anyway, because you're opening up a whole can of worms. Guys who've done this project have had issues on track. The mid-engined Integra that entered the SCC Ultimate Street Car competition suffered from poor braking (incorrect bias) and lateral grip (needed suspension tuning). There was a feature in Auto Italia a few years ago of another mid-engined build, full tube-frame, engine moved rearward... similar issues with balance... massive understeer on corner entry.
Mid- would be fun to do, but if you're doing it to cure a handling issue... no.
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