While I tend to lean toward building rapport early, I also understand that not every seller needs or cares about that.That said, I do think there are some sellers who care about more than just the money, they want to feel appreciated or comfortable with who they’re selling to.

Get out of your comfort zone.

I would say if 10k feels like a lot right now, then wait until you feel more comfortable.

You also have states like Indiana, Ohio, Florida, Nevada, all depending on your comfort level in distance or rental type.

The more I have researched the area, the more comfortable I am to actually do it.

Most will likely stick to the technical limit of Sept 2021 when it ceased being a primary residence, but some may be comfortable going by the address on the 2021 return and others may explore a partial exclusion, depending on the reasons for your move abroad.If you'd like to read up on the technical rules, the IRS publication 523 gets into more detail than most people would like to know, but it does have some helpful tables and examples for different scenarios.

I am super relaxed with 2 small children.  

You can choose to background check each of the occupants if that makes you feel more comfortable.

Accordingly it should come with everything needed for a comfortable short stay, which would definitely be utilities. 

That may help you feel more comfortable here or if it doesn't then I'd explore other quotes.