If you spend ~$40k more on United you might make it into Global Services, which will allow you to apply plus points to award travel (see here: Consolidated Global Services Thread: Benefits, Questions, Experiences [2021]) but sadly it isn't something 1k members can do...

I would look if you can shave down the number of required segments by adding more segments to existing flight reservations if you have them (same day change for more layovers), maybe then you can spend less money/time on a dedicated segment run.