As I said, if you are handy enough to make a proper tapered shim, routing the pocket is probably not a big deal. But that's a bit of a loaded statement on my part. A tapered shim isn't really that easy to make, despite what you see online.
Turn, If I wasn't an entire country down from you, I"d happily pay you to route out the neck pocket so it had a little angle and work as you described without shims....
I've written about this before. I own four basses...
98 EBMM SR5 Stingray
2000 MIM Fender Jazz V (converted to fretless)
2013 AM STD Precision V
2014 AM STD Jazz V
I've had to shim all of these basses so I wasn't bottoming the saddles on the bridge plate. In all cases, the B string and the G string saddles were sitting on the bridge plate before I shimmed them. Note that I wasn't trying to go any lower, but I noticed that when they were where I wanted them, they were either on the plate, or at least a 1/8" turn would have them sitting on the plate.
A single layer of business card is all it takes (on my instruments, anyway)
I use medium Ernie Ball Power Slinkys (050, 070, 085, 105, 135).
I DO NOT like a really low action. I like it just slightly higher than what the specs call for.
I adjust the necks so that there is a little relief, just enough to be able to tell, so the bridge saddles get adjusted a little lower (I guess that's the reason, I'm not a luthier by any stretch)
I've just resigned myself to be prepared to do this with a new bass, unless I happen upon a neck-through bass.