I think I initially cracked the LH portion when I pulled out the lower column trim. At least I'll know for next time. If I find another one, I'll have to do as you recommend to get the replacement in. I see where there are a few available but they are wanting between $225 and $325.
I'm a junkyard regular, and when I find them I charge less than that. I think I sold the last one for <$150; that was a pretty worn unit.
Currently there aren't any around locally. If you're open to painting one from a Cougar, that would expand your options; they come in grey, beige, etc. You can easily match the black finish of the Thunderbird with PlastiDip. I haven't tried Duplicolor Vinyl paint on these pieces, but I imagine that would work, too, and be more durable than PlastiDip.
Pulling the lower dash trim or lower column trim should not cause this. This trim is attached to the structure behind the lower dash trim. However, you might have hit this piece by trying to pry out the lower dash trim (?); that would do it.
If I find one, I can let you know before putting it up for sale. Let me know if you're open to painting a non-black unit. Also be aware that shipping these is expensive due to size and tons of shipping material plus you need to insure the shipment. USPS broke two of them for me... :-(
I do lower the column when I pull them in the yards. That said, I never do that on my car; the '97s come out a bit more easily.
General rule for installation: use rubber washers and/or fasten screws just barely. Tightly fastened screws cause the screw holes to break during changing temperatures. The upper screw holes are almost always broken; you can still fasten those screws by placing an appropriately sized rubber plug or cork stopper into those holes, then drive the screw through it.
The bottom screw holes are usually at least partly intact; you work with what you have.
The clip left and the three clips right are usually intact and not terribly fragile.
The screw holes for the defrost switch are fragile. Fasten screws gently! At removal, the defrost connector can be hard to disconnect; in that case, instead of disconnecting it, remove the defrost switch screws, remove the trim piece, and then remove the switch from the connector.