I'm not familiar with the solder/flux combination you're using.
In just over 40 years welding, I've used 45% silver braze wire and the white paste flux from welding supply houses on quite a lot of stainlesses. The melting temperature of this wire is approx 1145 deg F,,remelt temp is higher) and the flux has to match that temp. Chromium oxide forms readily on stainless surfaces and has to be mechanically removed by sanding, grinding, etc. After the surfaces are down to bare metal, and while the parts are at room temp, very lightly coat all surfaces to be bonded with the flux and position the handle and clamp it tightly to the bolt body. The rest is how I do it, and may not work well for anybody else..... I hold the bolt vertically, with the handle end up, in a vise with copper jaw softeners. wrap a wet shop rag around the bottom end with the locking lugs, and heat the bolt body below the handle with an Oxy-Acety torch. Set the flame on a #0 or #1 tip to a slight carburizing flame, that is with a feather about 1/8' past the conical flame. Move the torch continously and sometimes ease up onto the handle in the area to be bonded, but don't crowd the joint, stay at least 1/2' away from the surfaces. The flux will turn clear before you reach the melting temp of the wire. If the flux or any part of the joint turns a dry black color, the wire won't flow like it needs to. Try not to apply the flame directly over the wire, it will make it a lot harder to flow also. In good light, you may see the parts just begin to turn red. In low light the area will be visibly red. Dip the wire in the paste flux and try touching it to the top of the joint, away from the flame. When it's ready, it will flow so quickly into the joint that it seems to be sucked in instantly. If you get it right, you will see a small, bright wet fillet of liquid silver all around the joint. As soon as that happens, pull the torch away and don't try to reheat it. After 1 -2 minutes I take the bolt out CAREFULLY holding on to the wet rag at the bottom end and quickly dip it into water and out again. Don't leave it in the water. Just jab it in about an inch and jerk it back out. It'll pop off most of the hard flux and safely start to cool the back of the bolt down. You can repeat the quick dip several times, 10 - 20 seconds apart, and finally drop the whole bolt into the water and let it finish cooling. Remove the clamp and inspect the joint looking for the silver flow all around, then touch the very small fillet at the front of the joint with a small 'safed' file that will only cut the silver fillet without marking the bolt body. Jewelry makers use a lot of these files. Ideally, the fillet on this side will be so small that it won't need filing at all. Check the bolt in the receiver to verify that it's rotating into full battery,letting the bolt locking lugs fully engage the shoulders in the receiver). This is CRITICAL.
Three observations: you're right, chrome-moly bolts and handles are easier to silver braze than stainless.
2nd, There are people that offer this service. I don't. If I weren't comfortable doing it though, I wouldn't hesitate to send it to one of them myself.
3rd, It's possible that Remington would warranty the handle coming off. It shouldn't have -- and they should.
I got long-winded, but tried to get enough in to help.
Good luck, whatever you decide to do. Tom
