From what I can see in the pics that have been posted, I would say that the body does go with the neck. In particular the shape of the control cavity is familiar.
From the pics it certainly looks identical to the 1990 japanese '62 reissue Precision I used to own. I can't see the strap buttons clearly, but it looks like they might have been swapped out for staplock buttons. I recall there was also a 'hootenanny' strap button on the back of the headstock. It also looks like someone took a dislike to the finish on the back of the neck on yours for some reason.
I'm a big fan of my H2n, and use it to record every rehearsal and gig. I will probably wait for the next iteration of the h2 before thinking of upgrading, but the 32 bit float, usb-c, and bluetooth control look like worthwhile updates.
I have a blueburst one of these, its a great bass that I'd be using a lot more were it not for my three JMJ Mustangs.
There's no need to replace the tuners — I use LaBella's danelectro-specific set of flatwounds and they are perfect.
https://www.bassdirect.co.uk/product/la-bella-760-fd-dan-electro-stainless-flats/
I upgraded my main board to a spaceship power 50C which has the power pack built in and is powered via a kettle style power lead. I really like it and don't think there's anything similar on the market that touches it for the cost.
I've used their guitar strings in custom guages when I had a tenor guitar and tenor banjo which I set up in chicago tuning. I'd only be able to try their bass strings if they ever made stainless steel flats in short & medium scale though.
I don’t think that’ll help as I specifically wanted to fit the hipshot lollipop tuners. The wilkinsons currently fitted are as good a second choice as anything else.