I run a twin pallet vertical with a 30 tool magazine. I'm no systems expert and have worked alone forever, so that likely shades my processes.
1) Leave tools loaded if possible. Things like Spot Drills and Chamfers etc. A Facemill or two. I'm not able to leave many tools loaded as most the production pieces I run use too many tools. Especially when I'm always counting a Probe and Fan as two of them. But with 60 tools you might have a better chance of leaving a bunch mounted.
1a) If I could afford it I'd never completely tear down the tools in a job. (I might remove them from the machine, but not remove the tool from the Tool Holder.) But because I can't, I'll sometimes keep all the cutters for a job in a box saved for next time. At least ones that are critical and are attached to any Cutter Comped Tool Offsets. Clearance or other non-critical drills and roughing cutters not so much.
2) Before tearing down any job I punch out the Part Program and all of its Subroutines en mass as one file. (Fanuc Copy-A-Range w/comma)
3) Punch out the Tool Offsets
4) Punch out the Work Offsets.
When the job comes back, copy these three file back to the machine, and run the two offsets files to reload their settings. Now except for loading and measuring previously pulled tools, you're almost ready to go.
Then I'll run a Renishaw Automatic Part Setting Routine designed for that particular pallet arrangement and Work Offsets used. This routine will use the existing offsets that were loaded and update them accordingly. A thou here, a few tenths there etc. My setups generally consist of a bunch of pinned in place vises, so they're fairly repeatable. Still, I double check them with the probing routine each time.
I saw a YouTube video a couple years ago of a California company that took all the tools from every repeat job and stored them in racks in a room. To me that's the most sure fire way to get the job up and running and hitting all sizes quickly. I mean... having the exact same tools in the same holders that finished the previous run has got to be a step ahead.