Different generic brands may have different dyes and different substances mixed with the warfarin to make them into a pill.
I tried one a few years ago that I made it impossible to regulate my INR.
Your idea of putting the pill(s) into a capsule, and swallowing the capsule is a good one. You can get capsules at VitaminShoppe, online, and probably at some pharmacies. As long as the capsule is large enough to put the pill into, it should work well for you.
As far as chewing the pill, or mixing with applesauce, I don't think these are good ideas. The applesauce may dissolve the pill, making the whole mess taste even worse. Chewing the pill may change the way that it's absorbed into the system.
Have you tried putting a small sliver of bread - something small enough that you can swallow - around the pill and swallowed the pill? Maybe this will help.
I've been taking Coumadin, then Warfarin, for more than 30 years and can't remember EVER having the issue that you report.
(And I wouldn't rule out the psychological aspect -- especially if somewhere along the line, you were convinced that it was Rat Poison. The warfarin that they use to kill rats is much higher dose than any of us can take, and they've stopped using it because some rats have mutated so that they're warfarin resistant. Many of the things that we eat can be poisonous. You can't give a dog chocolate - to them, it's like a poison - but WE can eat it. Consider that the warfarin in Rat Poison might be slightly different chemically from the warfarin that humans take - to the rats, this modified warfarin can cause them to die (they get a massive dose that doesn't really 'poison' them - it just reduces their clotting time so that they bleed internally) - and that the warfarin you take, in such tiny doses, will help, rather than hurt.)