I put the hot rod set in an Epi LP that I have. I like the pickups better than the stock ones that were in it but the Jazz is, IMO, not that great and not a great companion to the JB, which is great.
On my Plus Top Epi LP I absorbed the extra cost and put in a nickel covered set including the JB bridge and '59 neck; and this turned out to satisfy me way more than the hot rodded set. This is a great pair in my opinion and I have put it in a few guitars since.
The '59 neck pickup far surpasses the jazz, as far as I'm concerned, especially in the area of holding together with a nice clean sound as well as sounding great when played into an overdriven amp. Chords sound very dynamic with the '59 and leads sound clear.
I still have the hot rodded set in that LP and I live with it and it is still a fun guitar to play. I make the most out of the jazz neck pickup but avoid getting any more of them and never intentionally buy one.
I played a nice deluxe LTD that had SD Alnico II Pro's in it and I thought that sound was very excellent. I just played that guitar again last week thru a real nice Marshall stack and reinforced how much I like that pickup set.
Looks like you have a lot of options as far as dealing with that neck pickup goes; and you have some other things to take care of with this guitar anyway.
That is a beautiful guitar, by the way. I really like that burst and the grain. When the scotchbrite treatment is finished on that guitar it might look really great. I don't mind the satin finish, personally. I think it looks good.