I am probably one of the few people here that shoot with a HID vid light only because I had to until yesterday
. For me it worked great because I'm not a photographer and didn't want to be overloaded with my first housing. The link I'm providing has pictures taken in St Croix. No, it's not murky Finnish waters but the vis at that time was bad. It looked like a snow storm most of the time which is evident in the pictures (Dsc01670_1.jpg, Dsc01693_1.jpg). Silt was covering not only the sponge's (still) but the seahorse as well.
With all that said, I'm not sure that the lights will provide you with a better picture. You mentioned that your pictures are overexposed. Are they "clear" and overexposed or is it the backscatter which is overexposing the picture. I believe the clear/overexposed can be taken care of by settings. Overexposure due to backscatter could be fixed by moving your arms outfarther and possibly forward as well as turning your strobes out a bit.
The other side is that using a vid light would take the guess work out of lighting your subject in your extreme condition as well as allowing you to see what the shot should look like.
I'll go back to lurking while the good photographers help solve your problem.