I never heard anything about Tuesdays being worse than other days, but the system being "wonky" is always a risk. Log in ahead of time, and have a backup (e.g., if you're using the app and are having trouble, try the website, and vice versa).
FWIW, Slinky FP+ are generally "sold out" 62 days ahead. Since you're visiting on Day 63 (Saturday being your day 60), if there is any availability for Slinky, it's likely to be in the late afternoon or evening, so plan ahead for that. Also, if it shows NO availability, try splitting up your party into smaller sizes (e.g., for a family of 4, try making two sets of FP for two with overlapping time windows), as smaller party sizes generally have greater availability.
Touringplans has a Fastpass availability tool that is helpful for trend-spotting and checking availability. Keep in mind, however, that it only checks for parties of 1.
https://touringplans.com/walt-disney-world/fastpass-availability