I wasn't able to replicate the interruption you mentioned and can confirm clients are able to continue adjusting search filters after reaching the three-invite limit. If a client further attempts to invite an additional freelancer, they would see a pop-up asking them to upgrade their job post or in your case, being a new client, ask you to add a billing method in order to access this option.
Note that you need to add a billing method before you can send an offer and hire freelancers you've communicated with (you haven't hired any of them yet).
Please review these resources created to aid new clients with using Upwork and let us know if you need further assistance.
James and Josh (the original poster), as freelancers we completely understand that 3 invites per job post is inadequate. We have, collectively, suggested that Upwork modify that number to no more than 10.
This 'test' arose because a very small percentage of buyers abuse the system and send out 75+ invites per job post. There is a vast difference between 10 or less and 75+.
Hopefully Upwork will amend the number of invites allowed to better serve both buyers and freelancers.
To address your concern regarding how payments are processed on Upwork, and which Payment Protections are in place for Upwork Clients, kindly check next help articles:
Let us know if you need any further assistance.
Clients who do not want to pay will simply go for intermediate freelancers (and prices) and the present system of making both parties pay is simply going to lead to circumvention.
I have been hiring Freelancers from Upwork for years (since odesk days) and have three separate accounts for three different businesses. The "trial for a small group" is BS as all my accounts have been limited. So not only are you charging me and the freelancers exorbitant rates, you now what the employers to pay $29.99 per job for the privilege of inviting people we feel are the best fit for our roles. I will not do it and will be leaving the Upwork site as soon as my current contracts have been completed. Being profitable is one thing, ripping people off is beyond acceptable.