Is there a place to access Final Cut Pro X on public computers?

Nope... You're going to need to buy a computer that can handle FCPX.

I guess, all your stuff is on the Macs internal drive...?

does your Mac offer usb3 ports?

then invest 50 bucks into an external 2.5" Harddrive and put your Lib onto that...

and avoid nonsense like compounds within compounds... often reason for 'stutter'

tech background: one platter has to deliver ALL compounded material simultanously...

and to answer your initial question: no, never heard of. Even renting a Mac is close to impossible.

best-of-all: for a long time, the Munich Applestore here had no FCPX on their demo machines.... but Facebook, all devices on display crowded by kids, "it's free!!" ... arrghgh 😠 Would like to see Mrs Ahrendts in a reality-check here... sorry, getting off topic........................

I think your best bet would be to find a friend who would let you finish your projects on their machine. Or if you have a local access cable station in your area, possibly contact them to see whether they use FCP X and whether you would be able to use it if you became a member. There's no harm in contacting your local library; at mine they have Photoshop, so who knows? As for the Apple Stores, I imagine it would depend on the store manager and how busy they were as to whether they might help you out . Years ago, I had a huge H.264 transcode that was bringing my PPC Mac to its knees and a local store took pity on me and let me complete it on their MP. But it was a one-time thing…I didn't set up camp there.

A final thought…You didn't specify a model for your laptop, but there are some things you can do that will speed up the process regardless of model. Make sure you have a minimum of 15% free space on your boot drive. If the RAM is upgradable, find out what the maximum amount it will take and install it. Store your media and libraries on an external drive, formatted OS X Extended (Journaled). USB3 and Thunderbolt drives are best, but if your Mac doesn't those protocols, Firewire 800 will probably be fine. Avoid USB2.

Good luck.

Russ

Public Library, mine offers modern iMacs

There are Macintosh computers at the Boise Public Library, too, but none of them have $300 Apple software products on them.

Since you have purchased FCPX, you could long onto the App Store on any Mac, using your credentials, and download FCPX to that machine.

Libraries aren't going to allow you to o that and they're not going to let you stay on a machine for the three or four weeks it will take you to edit your project.

PPut your FCP library and the application on a fast development and take to a fast machine.