i don't know quite a lot about what most of you are talking about, but in my opinion i'd completely forget about the pedal for now. your main concerns should be your amp and guitar, and then once you get them to your liking then i'd start playing around with pedals.
another thought, you originally stated that the pickup sounded much fuller and thicker, but not too much more distortion. i think you might just be expecting too much. i actually had the same exact problem as you. i bought my first bkp, plugged it in, and was like "well, this sounds exactly the same". i thought i had the wiring mixed up. the thing is, for me at least, there's not such an incredible difference that you'll immediately hear a dramatic difference. but now after i've had my new pickup for a while, it sounds so much better than my other guitars.
i know a lot of people on hear will tell you they immediately heard an incredible difference with their new pickup, but i think for some you just have to get used to it to appreciate it... especially when you don't have a lot of experience with difference equipment, like it sounds like is true for you.