I would think that would work great. Have you found a pump?
Home Depot, pond pumps...
I live in Kempner and have the same issues..
Swirling the prechiller water has to be done, for the same reason you need to move the wort around the chiller...
There is a thermal barrier that is created around the copper tube very quickly that "insulates" the copper tube from the cold water in the ice bath (or hot wart)
Stirling both the wort in the boil pot with the chiller and the ice water in the prechiller cooler at the same time is a pain... but it does work.. and I can get my 4gal boils down to pitching temp in under 20 min.
For my last batch I used a pump... I do not recirculate the water from chiller back to ice water container till wort temps come down to the 100 deg or so. Just run the water hose into the ice water container at a equal rate as the pump moves water from the container so level stays constant.
Once wort temps come down, the chiller output hose goes into the prechiller ice water cooler and the water hose is turned off.
At that point I just have to gently stir the wort..till Im at pitching temp.
I do top off my 4 gal boils with ice cold filtered water to eh 5.25 gal point,, so that further cools my wort for pitching.