I wish you had asked us here. Zero pressure to take our advice.
You can find older wrecked salvage bikes cheap (auction generally adds about $600 in fees to price):
https://www.ridesafely.com/en/salvage-c ... 9&rcppg=10 Bike dealers often know of wrecks for sale. Doesn't hurt to call around.
Just about any 400cc or larger bike motor will be more powerful than an antique kei, though you still have not told us what model it is.
I agree. A 520 chain offset, oil bath drop box with a tensioner shoe would solve that and provide a little more header room. Straight cut gear to gear would be noisy. However, if you raise the car an inch or two with the full frame, the clearance will improve. The original shaft is too small of an OD for the length to prevent whipping so you will need extra room. Also the miata diff flange may not be centered. I think it is toward the right side a 1/2 inch but it has been a long time since I checked. Plan on a 2.5-3 inch od shaft.
Look at a honda shadow 750 for being a shorter distance from the front of the head to the sprocket for sideways mounting plus the exhaust is on the side so it would exit forward instead of into the strut tower.
Look at a honda shadow 1100 for shaft drive and plenty of torque. The standard and cruiser bikes in a milder state of tune are better for installation in a car; less likely to surge at part throttle or need cush drives.
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Miata UBJ: ES-2074R('70s maz pickup)
Ford IFS
viewtopic.php?f=5&t=13225&p=134742Simple Spring select
viewtopic.php?f=5&t=11815LxWxHt
360LA 442E: 134.5x46x15
Lotus7:115x39x7.25
Tiger Avon:114x40x13.3-12.6
Champion/Book:114x42x11
Gibbs/Haynes:122x42x14
VoDou:113x44x14
McSorley 442:122x46x14
Collins 241:127x46x12