I'm going to dash your hopes to pieces right here. Only remote positions that a TM could move into are a handful of senior administrative assistant positions for a couple of the teams out of HQ. And they will take an existing admin assistant from a building or an external with experience over a WW or LWW.
Other than that TMs do not go to HQ or get Full-Time/Hybrid remote positions. OM's rarely get those positions. Usually its support OMs (TOMs, CI, ICQA Leader, PC etc), SOMs, SDs and w/e the store equivalents are that get those positions. You're interviewing with big shots that are usually only a couple levels below Cornell himself. Even SOMs interview with Group Directors and people the SD reports too.
The decisions you make on those teams affect not just your building but potentially the entire region and even the whole supply chain and your OM's opinion, even SOM's will carry zero weight. Most people are already doing work for those teams before they get the role and almost fast-tracked for the role.
Long story short you'll probably get zero response and if you do it'll be a polite no thanks.