First, I would completely eliminate Tultex from your list. It's just my opinion, so take it for what it's worth.
I've gotten different samples of Tultex over several years (just to see if they've gotten better), and using them for a brand that you would consider using AA for just won't work. They come apart *very* easily. They shrink at least a shirt size on the first wash, and they get hard and rigid.
If you really like AA, you need to consider how much you want to make from the sale of each shirt, and maybe price your shirts accordingly. You also may want to find better prices for AA.
If you're letting your printer source them for you, some printers charge WAY more for sourcing blanks than other printers. Shop different printers, and shop different blank vendors. Compare the prices of AA at different vendors and see who has the best pricing. Then see if you can find a printer that will print on your supplied AA shirts.
I've got wholesale accounts at several blank vendors, but I let my printer supply my AA shirts. They only charge about 50 cents more for AA than I would pay buying them myself.
Everyone is free to run their business as they see fit. But I'll tell you how I came to the conclusion of paying the extra $ for AA. Take your Gildan shirt for example. If the Gildan is $2 less than AA, is paying the extra $2 per shirt worth it to your brand? Can you charge an extra $2 to your customer and they know that the shirt is worth at least $2 more if you had used what you perceive to be a lesser quality shirt?
For me, the price difference didn't justify using what I perceived to be a lesser quality shirt. I don't know what price point you retail your shirts for, but if you charged $21.99 instead of $19.99 (or $26 instead of $24?) and used what you perceived to be a better shirt for your brand, would that $2 break you or your brand? Your customer just paid the price difference.
Or better yet, can you sell at what you want your price point to be, and still be successful? For me I could. Making $2 less per shirt wasn't going to ruin my business or my profit. Every shirt I sell is almost 4 times what I have in the shirt. So, paying $2 more for AA gives me a better shirt (in my opinion), which is better for my brand, and I can still make a decent profit.
My advice to you is to find the best blank that works for you, and see if you can make the retail price point justify the price of the blank.