Hey Shayna,
There's definitely a way to replace a single panel of click-in flooring, I know repairmen that would do that. I would leave the damaged flooring in place for now, explaining to the new tenant that you need to hire a professional to replace it, and that it will be a few weeks before they can come. Most tenant will agree to something like that, as long as they know a fix will happen relatively soon. I'm building my second Missoula ADU right now, they're pretty sweet little projects!
Below are my recommendations for local guys who could take on something like this, I'm happy to answer additional questions about them.
Jerimiah Purdham- Does good work, but usually booked out at least a month. Charges $50 per hour starting this winter
Joel Deming - (406) 493-7410- Local investor Liz Beaird says "Joel Deming all day long!"- He said "I've done flooring, some plumbing, some electrical, some drywall. I have experience with heavy equipment and heavy construction as well."
Jeremy- 406-560-7070- Does a good job tiling, did bathroom at my current house. Does all types of flooring.
Nick Pantaloni - (406) 830-4109. Local realtor Megan Robson recommends them. They do really lovely work on smaller projects and remodels, but they're completely capable of doing larger stuff too.