The idea I had would have resulted in the search panel remaining on-screen at a place you specified but in testing it failed because of this: when the prompt is up on the screen, if you click away from it (to bring another window or app frontmost for example) the prompt disappears and doesn't return until you trigger the macro again. This is a feature of the Prompt for List action and I queried Peter about making it optional but he has no plans to do so.
All is not lost, however, as @noisneil has already written a macro that is the equivalent of Prompt with List and is called Prompt with List (HTML) that optionally will remain on-screen until deliberately dismissed. I am pretty sure that my idea plus Neil's macro can be made to achieve your requirement.
It's now too late for me to take this any further until after the holiday break so if you can wait I'll resume in a few days time.
Meanwhile Ronald, have a merry Christmas 
Addendum:
Just FYI this is a description of what I did to your macro that came so very close to working!
The changes I've made to your macro are very simple as follows:
- Engroup your two actions Prompt with List and $If Macro Group Active with an Execute Actions Until Conditions Met action (coloured teal in the screenshot)
- Insert a Set Next Engine Window action before the Prompt with List action. This will allow you to specify where on your screen the search pane should sit.
- Set the end condition for the Execute... group to be a variable condition that checks for Local__Result variable being empty.
(I can't add the screenshots as I'm not at my Mac.)