Hi Ben,
Your idea would be the best way, however, after testing, this way currently has obstacles so that it cannot be implemented.
Here is my test steps.
1. I have a Contact BPF with 4 stages.

2. I add the Contact BPF on the site map.

3. I set the Contact BPF control to eidtable grid.

4. On the Contact BPF view, it seems to allow us to change the Active Stage, but when we select another Active Stage, there is no options. This means that we cannot modify the stage in the view of the eidtable grid.

In short, by adding Contact BPF to the site map, we can see the contacts and its stage in the grid, but we cannot directly change it by editable grid control.
So to change contacts stage quickly, we have to create some on-demand workflows, or we can use the tool of XrmToolBox.
Solution 1. on-demand workflow
Set the workflow as follow.

Select the active stage in the update record step.

we will create one on-demand workflow for each stage, if there are 4 stages of Contact BPF, then create 4 on-demand workflow.
Go back to Contact BPF view, select the contacts records, then click Flow > the workflow of a stage. In this way, the selected contacts will be changed to the stage of the workflow.

Solution 2. BPF Manager of XrmToolBox
This is the download page of XrmToolBox: https://www.xrmtoolbox.com/
After decompressing XrmToolBox, open XrmToolBox. exe.
Use your account to connect to the D365 organization. Install the "BPF Manager" tool.
Open "BPF Manager" tool, we can update the stage of some records in bulk.
