I got the new replacement chain brake handle. It took about a week, but before delivery I started thinking. The part that broke off on the handle was the plastic trigger on the chain side that launches and releases the break lever. Could I replace that alone with a shop-made part? I figured I had nothing to lose because as it stood, the handle was toast.
Here's what I did. I drilled a hole from the outside slightly smaller than an M-5 metric machine screw right where the plastic part snapped off. The screw I found in my spare parts is about an inch long. Next I threaded that screw into place and added a jam nut tight to the handle. Lo and behold, that was strong enough to allow both a lock and an unlock of the chain brake.
Before I install the new handle, this repair has to fail. My gut feeling is that it will not fail very soon. Time will tell.