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. 

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 ‘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