I dislike the JP blocks for various reasons, including but not limited to the fact that it has no locking mechanism as shipped from the factory which basically means it was meant to be "set" at its sweet spot for a particular load/conditions and then loc-tited in place. If you don't do that, they will eventually work lose/fall out but probably not before the rifle is overgassed and in need of "readjustment" anyway. Its the same old, tired design JP has had in adjustable blocks for over a decade now and pales in comparison with other offerings currently available on the market. Thus, if it were mine, I would happily ditch the JP block for a different option. I certainly wouldn't go hacking up the SWS handguard, especially since you've already gone to the trouble/expense of having it Cerakoted (which will have to be redone if you go at it with a Dremel/etc. to modify it to fit around the JP block/screws).
Now, with that said, how much room does your current SWS have in terms of ID top to bottom and side to side (I can't recall if the SWS is perfectly round on the inside or not)? I ask because the options for a 0.936" adjustable block are extremely limited and not nearly as plentiful as say the 0.750" or even 0.875" blocks. Furthermore, with a barrel/journal that large in diameter, getting ANY block to fit UNDER a handguard is a tall order on even some of the larger ID tubes like the Seekins BAR, etc. which measure up to 1.8".
At the moment, you have the SLR Rifleworks block which is the best available currently in my experience. They offer both a set-screw and a clamp-on block in 0.936" depending on how your barrel is setup. For a precision AR, the clamp on is a better option, but larger thanks to the addt'l room needed for the clamping screw/mount. You have everything in hand so taking the measurements shouldn't be too difficult. Here's a link to the SLR site...you'll see the 0.936" blocks toward the bottom of the page:
Gas Blocks
There is also the PRI and Wilson Combat adjustable blocks in that size, BUT...they will NOT fit under any handguard I have looked at with them. YMMV depending on the size of the SWS handguard, but I'm doubting it.
Now, if you don't mind giving up the adjustable block, there are a host of options for low profile blocks, with the smallest being the Troy Industries 0.936" gas block.