Noise Reduction for Bosstone?

So, I have a Jordan Bosstone. One day I decided to listen to it (hadn't for many years...I kinda found it in a had been long forgotten.)

I loved it...So, in light of not wanting to hack up a vintage bit of gear, I made a pedal-form clone.

Well, it isn't the quietest effect ever, so, I was hoping to get some input from everyone. Do you think I could reduce the noise floor (which is fairly high) by using a small isolation transformer in the signal chain?

I can't remember the Mouser # but it's one of those little 1:1 ones...that you could use for a DI.