That thing in going to take a giant shit at load. Don't take my word for it. Try and see. You'll probably need two of them on on large block to accomplish anything worth while. You can build a pretty simple PWM controller for your TEC using a MIC502 Fan PWM IC and a few ancillary parts.
As you have already found out, it's not how much heat a TEC can move. It's how much it can move at delta T that matters. You will have to use multiple TECs. You would be better off making a TEC water cooler, where you can use a large number of them together to raise COP.