Assuming you do not need a traction tire of too much sort, the Toyo and firestone ht models have done me well. No neither has the same traction of an at, but still overall dang good if on dry to rain wetted roads. If you get into slimy dirt, snow etc, yes, all bets are off on going forward or not. You did mention you have a second set of winter tires, so these may work.
I'm also running a discount tire at right now. To me, more of an aggressive why tire. Not bad in snow last winter. Have had better snow traction ok n tires, but worked. 60k mileage warranty, with 8000 miles, show little wear. Not bad for.one of the cheapest tires I found in a 245-75-16 at $125 per, vs most in the 150-200 range.
I concur with some, michiblows are last on my list of brands to buy. Cooper and toyo are usual first choices.
Marty