I got it down to three widgets:
It DOESN’T work for me on 2021.2 but I sent it to @klincecum and he got it work on 2022.11.
The trick is in the Fill Table by Query. When executing the BAQ, one of the parameters is the Execution Dataset. This dataset holds the parameters and their values. So, how can we fill that table? Well, the query itself has a list of all the parameters, so I use that as the source to fill the Execution dataset. The mapping is straightforward:
To set the parameter value, I use an expression that changes value for each parameter:
Here I am assigning the function parameters (P1, P2) to the BAQ Parameters (Parm1, Parm2) but they could be Function Variables or maybe even BPMData.
You have to have an expression for each parameter, and nest them. In 2021.2. this hasn’t worked for me. Any variables I tried return null. Maybe it’s a known bug 
but as I said, Kevin was kind enough to try it on his system, and he was able to get it to work.
Yes @JasonMcD, widgets can be fun!
DEMO.efxb (183.0 KB)
DEV-ABC.baq (13.3 KB)