April 1-11- the first three days shouldn’t be insane, but starting on the 4th it’ll be insanely crowded. But if you’re going by yourself, you know your way around the parks and try not to backtrack much, are willing to pack snacks/eat meals at off times or at sit downs, and are good with refreshing to obtain many same day fp, you can still have a good time and get a lot done. Just be prepared to not walk anywhere quickly, wait for bathrooms, long security lines, etc. Any Disney trip where the actual travel is paid for by your company is better than no Disney trip, regardless of crowd level.
October isn’t exactly slow anymore anyways. It’s one of the busier months. The parties and food and wine festival have done an excellent job at increasing attendance. Plus, some schools/colleges have an October break. Keep in mind that October is still the middle of hurricane season though, which means there’s a chance the weather could be awful and/or the parks could close.