Ultimately, only you can decide which instrument you bond with, and which you prefer the sound / feel of...
I would say that everything you've described so far, ought to be addressable by adjusting the instrument's setup - be that slightly lowering the bridge saddles on the E string / raising the E A side of the pickup a little / verifying that the nut is at spec. Checking that the weak E is not an EQ / room issue, by recording it DI, and comparing it on different speakers, in different rooms / different headphones etc.
Have you setup the instrument according to Ernie Ball Music Man's Stingray setup specifications?
Now that you know the neck pickup is not intended to sound anything like the regular Stingray bridge pickup - is that a problem for you?
Do you like the sound it makes / will you have a use for it?
The bridge pickup on your HH will sound identical to the pickup on the single H model you've been offered in exchange - so is there any advantage to you making that exchange, or are you just loosing all those other available tones, simply because they aren't the exact tones you expected them to be?