LoneWolfGal, I have a cherry picker, and also the lift table that you already have and would like to share what worked out for me with the car on jack stands.
Since you will have a limited clearance between the floor and the chassis, if you put the engine/gearbox on the table lift, unfortunately it will not clear the frame.. and this process worked out for me.
Once the car is on four jack stands (high and level) then you can 'slide' the engine/gearbox from the back using a furniture dolly, or two large card boxes in top of each other so one would slide on top of the other one
After you get the powertrain underneath the car, you can lift it with the cherry picker so you can put the lift table underneath the engine, then you remove the engine, but to have more clearance I built a simple home made lift using Home Depot parts (less than $20..) and this thing would allow you to hang the engine/gearbox from the top and by turning the nut you can fine tune it (up-down) so you can easily bolt the gearbox and engine mounts.
The cherry picker is only used to raise the engine/gearbox after they are under the car and also to move the assembly around the garage
