What is the raw water pH?
How much iron and hardness?
Is this "sulfur" odor in both the hot and cold water or just the hot?
Slime means IRB (iron reducing bacteria), not SRB. You probably have naturally occurring H2S gas and IRB.
A chlorination system will not harm a septic system. I suggest an inline erosion pellet chlorinator, mixing/retention tank followed by a carbon filter using special carbon. And you don't have to babysit an inline chlorinator (at all) like you constantly do with solution feeders.
Using a chlorination system including carbon, does not allow chlorine by product problems but, very few wells have the right water quality (high organic content) to cause THM by products.
Why don't you want to be a DIYer and buy online and install it yourself instead of spending a small fortune for proprietary equipment that only the one'n only local national brand dealer can service and get parts for? Or do you want to be an independent DIYer and that's why you're here?