Hand 1)
Do you have reads that he doesn't value bet thinly? I think if we have that read, then I like the river call. Without that read, he has about 4-5 possible bricked fd's (KQs, KJs, JTs, QJs, KTs), and a ton of possible value shoving hands: AQ(12), AJ(12), maybe some A8s (1 or 2).

Hand 2)
I played a hand similar to this with A4s (QxxhhxA board - facing triple) and I value towned myself exactly like this facing a check vs AJs on the river.

I did some GTO on this spot to see how AJx checking the river would fare vs my shoving range and how KK would fare vs my shoving range, to see if either hand would be indifferent to calling or folding. Indifferent in your spot would be, being about 26% vs your shoving range.

In my spot, AJ had around 46% vs my shoving range. I didn't have much air, because most of my FD's on Qxx were folding turn except for some Kxs and Axs, and Ax got there. Also my shoving range assumed shoving all Ax.

In that spot, KK had around 26% vs that same shoving range. So that's the indifference point for your hand.

So if you think he's the type that would mostly shove AJ/AQ here, but check re-eval KK/QQ, then I think shoving is not bad here.