No matter what, the jack/shelf solution would require me to balance on a ladder 6-7 ft. off the floor while moving bikes from jack to shelf and then balance them as well as myself while I attached tie-downs. That sounds like a 400 lb. accident waiting to happen.
At that price for a 4-post car lift, it's probably the best approach in your situation. I continually underestimate how cheap machine shop and garage toys are over there.
Make sure you have a solid, well supported floor on the lift, with sufficient tie-down points.
On the mezzanine front, that's why you need enough floor width to provide a landing stage on the mezzanine floor, and a securely attached lift platform on the pallet lifter.
- strap the bike down onto the lift platform
- raise the platform to just above mezzanine floor height
- push the lifter to position the lift platform above the mezzanine landing stage
- lower the lift platform to sit on the landing stage
- climb up steps to mezzanine level (ladders are so passe)
- release tie-down straps
- push motorcycle carcass into position
Having the full lift platform on the landing stage (pallet lifter perpendicular to the landing stage) is safest, but requires more fiddly manouvring. Having about 1/4 of the lift platform on the landing stage (pallet lifter parallel to the landing stage) allows a straight push into position and a narrower landing stage.