Okay, it's fixed, sort of.
Considering you've already experimented with the Home key and tried remapping it, you might want to check all the other Internet keys too to make sure it's not just an issue with your failed remapping attempt.
The keys should be: Browser_Home, Browser_Back, Browser_Forward and Browser_Search respectively.
I had actually done that already, only I didn't know what I was looking at when I analyzed the results.
It turns out that the browser control keys on the Freestyle do
not send the standard scancodes associated with those keys. Instead, they send Alt combinations: Alt-Home for www home, Alt-LeftArrow for Back, Alt-RightArrow for Forward, and WindowsKey-F for Search. The unfortunate coincidence here is that this allows any of these keys to work much like Alt itself, i.e. Back-Tab will do the same thing as Alt-Tab. It took me way too long to figure this out, but when I did, everything became clear. In reality, my modifications using Keytweak and Sharpkeys never made the slightest difference to anything! I only thought they did because I didn't try subbing Home for Alt until I had made them. So I labored long under the misimpression that my "modifications" were "not going away," when in reality there were no modifications; what I described is how it works out of the box.
Armed with this knowledge, I placed the following in an AHK script:
!Home::Alt
; Maps Alt-Home to Alt
Now this does not make Home work 100% like an Alt key, probably because the system sees a double-press of the Alt key. But it does suppress the www home key function and allow Alt-Tab and other held-down combinations to work, which is all I care about.
Thanks for helping me get this sorted.