The ‘55 has no front cross member trans. support, only rear.  Thus the bell-housing/trans assembly must be somehow supported when the engine is pulled.  The author of the latest Y-Block engine book suggests removing the hood, and pushing the car back to get the motor off the trans. splines, which would require whatever support is under the bell-housing should then be mobile.  It seems to me that a simpler solution would likely be some sort of Jerry-rigged crossmember support attached to the frame rails (?).
I have a small rolling floor jack that could support the bell-housing, but not sure it could be reached/adjusted from under the car when the engine weight is removed and the suspension thus elevated.  Since I’m not sure my cherry-picker hoist will even have the elevation to raise the engine enough to clear the front nose panel, let alone the fender, I HAD assumed I could just remove the front wheels, and lower the car onto blocks (supporting the trans.), and then merely push the hoist forward, which would insure fender clearance and also permit leaving the hood in place. Not something necessarily recommended to be attempted solo, though I know it has been done.
However I decide to proceed, I’m sure some unexpected glitch will rear it’s ugly head, leaving me flummoxed, and at the worst possible time (Murphy’s Law) 😫

6 VOLTS/POS. GRD. NW INDIANA

I have used a ratchet strap tie down to support the front of the trans the last time I did an engine change.  Ran it from frame side to frame side.  Worked very well.

54 Victoria 312;  48 Ford Conv 302, 56 Bird 312
Forever Ford
Midland Park, NJ

The 1955 Ford Car Shop Manual has step-by-step instructions for removing the engine without the transmission for a 1955 Thunderbird. The manual has been reproduced as is readily available from Classic Ford/Thunderbird parts suppliers. 

Ratchet Strap. I just did my 56 Fairlane using One to support Trans while Engine is out.

  

Perhaps this may work?

https://www.harborfreight.com/1000-lb-capacity-engine-support-bar-96524.html

I used a piece of 1x2 wood slightly longer than the width of the frame rails outside to  outside and two pieces of all thread about a foot long, size doesn't matter, I  think I  used 5/16.  About 1 inch from one end, bend the all thread a little more than 90 degrees.  Hook these ends into the tooling holes on the  insides of the  frame rails near the front of the trans, put the all thread into appropriate holes in the board, put a flat washer and nut on the ends of the all thread, run the nuts up to support the front of the transmission where you want it, and all is  well..

John - "The Hoosier Hurricane"

Transmission jack. Mine has nylon straps to secure the transmission to the jack.

The shop manual instructions are rather confused, in that they direct removal of the clutch operating assembly parts, as if the bell-housing was being removed with engine (including trans. bolt torque #s), yet also direct the extraction of bell-housing bolts & dowels. Am I wrong, or can’t the block/clutch be removed/reinstalled without disturbing the throwout operating parts (?).

6 VOLTS/POS. GRD. NW INDIANA

My preference to removing a Y engine from a standard transmission equipped car is to unbolt the four bolts that attach the bellhousing from the engine and disconnect the clutch Z-bar pivot from the block.  The engine coming forward then allows the tranny with the bellhousing still attached to it to remain in the chassis.  A jack under the transmission keeps it from dropping too much.

Lorena, Texas (South of Waco)

6 VOLTS/POS. GRD. NW INDIANA