Hello,
that requires a customization, what you describe wanting to do.
The original GDV1 version of claim listing did not have the option to require payment for the listing to claim.
Now GDV2 has this option, to allow automatic claim if the user purchases a package, but the process is still optimized for a new user claiming the listing and then waiting for claim approval.
As you say, first they must fill the claim form, then the checkout information. Also as you say, if the user wants to purchase now, it makes sense to enter the appropriate info one time.
However, it also makes sense to collect the user’s information about the claim as early as possible.
One thing you can do now would be to use the Ninja Claim Form, and then you can refer to the NF plugin for changing the form, or adding a separate link to it.
Are you using WP Invoicing? If so you can post your idea about autopopulation here: https://wpinvoicing.com/support/