What sometimes helped the front finally downshift was, if I radically crossed the chain by shifting the rear to the biggest/innermost cog while the front was still on the big ring, with the FD grinding against it.
That sounds to me like you need to back off the inside limit screw just a tiny bit. Try riding uphill again, and repeat until you find that "sweet spot" where it shifts correctly without throwing the chain off to the inside. Test at both ranges in the back; both uphill and "zero load" on level ground.
I have an old Huffy MTB that I use to pull my son's trailer bike. We don't go very fast, and sometimes I have to change gears going uphill slugging along at low speeds.
What has impressed me is the fact that the cheap Falcon FD and RD shift fine under load both front and back. Like others mentioned; I had always heard you should back off a touch when shifting; that isn't possible with our "tractor trailer"; but it shifts fine anyway. Maybe its the steel cogs that don't flex? At times; I wish the nicer setup on my Viscount shifted as well.
-James