two things
thing #1: if you add a JumpStop or Cateye Chain Watcher to your seat tube, you can adjust the low limit screw further in, to the point that the chain would shoot on past the granny ring and derail were it not for the presence of one or the other of the aforementioned devices. With one of those in place, the derailleur forcefully slams the chain inward, the chain hits the device and falls unfailingly onto the granny ring, every time with no hesitation. I use them on all my bikes. Some teams in Le Tour also run them on their bikes to guarantee flawless downshifting with zero chance of dropping the chain off the inside ring.
thing #2: SunTour had the problem solved a decade-plus ago, with a front derailleur that worked opposite all existing ones. Instead of relying spring tension to initiate downshifts to the smaller rings, it worked in reverse and used the cable pull to downshift, and spring tension to upshift to the big ring. That way by pushing on the thumbshifter you could always get the thing to downshift even if it was coated in mud or ice. Real good idea. Now we have a similar idea for Rapidrise rear derailleur from shitmano, only that's a real bad idea for the same reason SunTour's was a good idea. With rapidrise, the critical downshift to a larger easier gear, a critical make or break shift on the steeps, is no longer controled by pulling the cable. Instead it relies on a spring, and a wimpy one at that, so when you need to shift to an easier gear RIGHT NOW lest you wobble to a halt on a steep climb, you better hope there's no mud or ice on the derailleur to interfere with the wimpy spring doing its job.
Point of this rant is, you can still occasionally find the old reverse action SunTour front derailleurs at places that deal in older stuff like that. One of them would solve you problem without the need for a jumpstop type device. I got some myself and ain't gonna part with them. try
www.bikeman.com, or of course ebay.