I had everything from BB414 (upgrade DiMarzio ModelP) BB614 (upgrade on/off) and more
Had both Ibanez Sr Premium 1200 and XXV anniversary
First of all, usually Yamaha necks are up to get tweaked to insanely low action. Now the problem is: did you lower the pickups height (especially bridge ceramic blade) accordingly?
That's main cause of them "poppin'" while hard hittin' (I had to do that)
For the sound you're after, better go with a Yamaha BB1024...
more Precision wise like you seem quite easily accustomed to.
Sr1200 stay unexpectedly near tho in this sense its Nordstrand
Big Singles make it for a very Jazzy (snappy) approach in passive mode and sit thru a mix with ease.
l'innocenza e l'intelligenza nel miracolo della Creazione.