I'd like to have that on a pull cable from the driver seat.
For tailgaters and upcoming unavoidable collitions.

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One thing I like about yours and the one gnob made were when you swing it down you can easily toss the tire on, boltup and then swing back up.
Rather than sopporting the tyre from the bottom would you not think about supporting on the wheel stud holes in the centre of the wheel.
Only thinking that with the pulley system mounting on the middle of the upper arm ( for want of a better description), the lower support is likely to keep catching the tyre as you lift it. A centre wheel stud mount would stick out less and be less likely to catch I reckon.
Not necessary in the top arm, but an option would be a front to back slot with a pin in it, The pin would be what you hook the rope hoist to, and then it could slide forward and back. But I'm guessing that if you just put the hoist attachment out far enough that the tire isn't banging into the bumper too bad while lifting, swinging it into the lower 'basket' wouldn't be too difficult.
Those pulley systems you referred back to a while back look great but I'd change the rope from that s***ty nylon stuff ( its too slippery) to some sailing quality non stretch rope.
Oh and add a cleat so you can tie the rope off easily with one hand.