Thanks for your advice! We ended up booking the trip. I figure that if a company would withdraw a job offer based on needing to give me 7-8 days off early on, they're probably not a good place to work anyway.
Blondeshania, that would've been good to ask! This workplace seems really disorganised. Along with pushing back the hiring decision repeatedly, they weren't able to tell me in the first phone screen what the hiring process would be or even what exactly I'd be doing day to day in the new role. So I'm not shocked they didn't think to ask that, haha.