I was in the US recently and played some JP7 with Piezo, and I found the same thing.
My guess is that it is "muddier" because the frequencies of the 7th string are very low for the piezo to sound "as good as it does" with the other 6 strings...
It doesn't seem as clear on the 'low B' to my ear, I found a few posts on this forum with others stating the same. It seems to happen after you use the trem a lot. So for example if I dive bombed a bit on a session and them went to use the piezo another time it could then sound like this.
Others have stated that diving the trem seems to clear it up again...
You probably had the action too low. The piezo will magnify string buzz much more so than a magnetic pickup. I have to keep the action on my bari a little higher than usual to compensate for this. I have that guitar in B with a .63 for the low B.
On the low B, yes. A big string has trouble keeping contact when diving the trem. Doesn't happen on my standard tuned JP's w/ .10's on them unless you go crazy.