Do I have space in the main panel for a 60 amp double pole breaker?
The ordinary generic answer for a short sub-panel run would be to relocate two 120V breakers or 1 240 V breaker to the sub-panel, sized appropriately for those additional loads.

But you have a FPE Stab-Lok panel, so you should replace it before it catches on fire, and when you do, buy enough spaces in that new main panel.

The house you save will be your own. One of many stories:

https://www.washingtonpost.com/lifestyle/home/despite-previous-safety-concerns-this-circuit-breaker-is-still-in-homes/2018/05/08/8927af86-4ef9-11e8-b725-92c89fe3ca4c_story.html