You should not have any problems using the correct puller; however, you might have considered buying the correct installation tool while you were at it. I realize that no one likes spending money on tools that seldom will be used, but sometimes you're money-ahead by doing so. Having the right tool saves time & prevents damage. 

I forgot about using an impact wrench to loosen the bolt. Definitely needed to remove the radiator. 

Unlike the car and truck FYB dampers where the timing marks are located on the damper ring, the timing marks on the Thunderbird damper are locked to the pulley.  The T-Bird damper ring is located behind the belt pulley and in front of the timing cover. The damper ring is ‘rubber’ mounted and can fail with age.
 

Are you missing the bolt or just want to know socket size? The socket size is 13/16ths. I recommend you use the correct puller when removing the dampener. Damper Dudes said that mine was in better shape than most they receive because I didn't use a hammer to remove it. The correct puller & replacement bolt (if needed) are available from Tbird parts suppliers. 

You do not have to remove the oil pan, but you do need to remove the front bolts that are attached to the pan & front motor mount. You'll need to support the engine while removing the timing cover. If you can remove the dampener without removing the radiator, you won't need to remove the radiator to remove the timing cover. My radiator was already removed when I removed the dampener.