faculty interviews - timing/conflicts
You can ask for an earlier interview, but they may have already scheduled someone for that time block and may not be able to accommodate the request.

As far as the resources go, it’s definitely an “early bird gets the worm” situation when it comes to faculty hires. Schools that delay their interviews run the risk of losing out on good candidates. So I would proceed on good faith: accept the interview, but let them know ASAP if you receive another offer that you intend to accept.