Well the build is on making a table lift for the bike, you could call this stage 1.
I've been looking at the lifts then thought hell I could make one so it begins. I did check first with my insurance first though I asked the Q,....."if I was to be working on my bike off the lift table and it fell off would I be covered" they put me on hold and came back with a yes I would.
I'll add more pic as it progresses, I'm not busting my chops on it
I would add a cross plate at the point of the forward casters on the floor jack. The plate should be welded to the lower main frame of the lift assembly. This way you'll be lifting, or spreading between two points on the lift, not the floor and the lift. Without the cross plate you're really only then supporting the weight of the lift/bike on the jack lift pad and it could tip.
Just one more piece of 1/4"x6" full width will do it for you. Also on that same cross plate, weld a couple short pieces of 1" angle iron 1" long vertical and they will guide and locate the two from casters so you know you're in the right place to lift.
But depending on how you have your lift upper cross bar places, when your jack goes up, the jack pad will come back towards you, but the cross lift bar should also come back as you're lifting, so they may stay in sync. Check that out before you get too carried away.
Good luck with the project.