Selling/Scheduling School Tours Online - Sending an Invoice

About to dig into this but I was wondering if any orgs are currently doing this and have some tips -

We are making our custom school tours available online through Tessitura/Tnew - virtual for now, in person eventually. We've set up a test date here.

https://engage.clevelandart.org/0/5362

We have pay-what-you can pricing, and regular pricing. However, we'd also like for the contact scheduling the tour to be able to request an invoice rather than pay online with a credit card. 

One option would be a $0 ticket price type "Send me an invoice" - but if I understand it's possible to sell a ticket as invoiced and then when the school district's check arrives, apply that payment to the invoice?

Thanks in advance!

Jim