Yeah, it could be the baseplate; my uncovered Mules would not fit into a standard humbucker rout until I slightly filed off the (very sharp and square) corners of the baseplate.
I checked the pickup, the baseplate dimensions are smaller than the cover. Of course I won't change anything without completely talking this through with the guys from BKP. Meanwhile they where nice enought to e-mail me back outside office hours asking the exact problem. It turns out that they have never encountered this problem before. In fact, I found a site with foto's of someone that build the exact same cover into his JP7. Perhaps the JP70 guitars are routed differently. I'm either going to modify this pickup but I would like to know first if it is possible to return the pickup so they can send me a open humbucker back.
So far so good!
Thanks for all the support guys! After having this problem I was very disappointed but I feel very confident that this is going to work out just fine!
PS.
Moderators of BKP, the sun is not yellow, its white...