Fold vs this villain.
For raise-calling to be better than raise-folding with QxTx @ 11BB, villain needs to be 3b jamming > top 23% of hands.
Expectation of raise-calling vs top X % 3b Jam range:

 
[3b Jam]

 
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%

S = 11.0
-1.8
-1.2
-0.6
-0.2
0.5
0.7
1.1
1.5
1.7
2.1

 
Against nitfish villains you make so much from the fold equity it's probably still better to raise-fold but limping wouldn't be bad either because he's not going attack you without a hand you're behind and your hand plays so well postflop vs his check vs limp range.

QTs is almost never a minr/fold at any depth (turns out even 25bb it's a call vs the PokerStars population at around the $30-$100 stake level!), This is 11bb deep it's a snap call--even if villain is shoving: QQ-22,A2+ it's .75bb better called than folded.

QQ-22,A7s+,A6o+
still a call

QQ-22,A8s+,A9o+
still a call!
22+,A8s+,A9o+ (now has KK-AA)
Now it's finally not a call, but is still only .15bb worse so not that big of a deal.
Not sure where you're going wrong cdon, but I think the major thing is that no one shoves top X% of hands (and top X% is usually a pretty bad ordering fwiw), you can always exclude big PP and you they shove more Ax and low PP than most top X% ranges shows. It's interesting though because adding in KQ does change a fair bit. But even so, vs a fairly tight 14.5% range
QQ-22,A6s+,A8o+,KJs+,KQo
QTs is still a call.

You need to have a ton of stuff like QJ KT and not as much low Ax and low PP to make QTs a fold. I don't think that's very realistic.