This was a live $70 MTT. I had built up my stack at a previous table to 27,000 when the average stack at the tournament was 22,000. Half the players are gone. The blinds were 400/800 with 100 ante, for a starting pot of 2200.
This is my very first hand at this table. I looked down in the HJ to find ATo and I raised it to 2200. I was called by the Dealer and the BB. The pot was now 8000. The flop came 89Jr. The BB checked and I fired out a semi-bluff continuation bet of 4200, for about 1/2 pot. I did this for several reasons:
1. This move helped me build up my stack at the previous table.
2. It’s a standard c-bet regardless of whether or not I hit, and being first in gives me fold equity
3. The flop was actually pretty good for me, so I had card equity too.

The Dealer, who had a bigger stack than I did, called without hesitation. The BB folded. The pot is now 16,400, and I had 20,600
The turn was a Q, so I had hit my straight. I figured at this point that the Dealer had two pair, trips, or was just really stubborn with a solid pair (it was hard to gauge what he had since it was my first hand at the table. I bet out for 8,000 and in retrospect I should have bet closer to the size of the pot and gotten him out. But 8,000 was the biggest bet I’d seen all day, so it seemed huge to me. My opponent called instantly. The pot was now 32,400 and I had 12,600 left.
The river was another Q, so any trips or Qx two pair now boated up. I checked and my opponent shoved AI. I was being offered a 45,000 pot and it was my last 12,600 to call. I was almost certain that I was beat, but the odds were so huge and I’d just bet 60% of my stack already.

Thoughts?

c-bet shove the river. nh

Yea shove the river yourself.
You can't consider folding given your SPR & the way villain played the hand.

Should I have shoved the turn?

yes

But that means I'm overbetting the pot by just shoving 20,600 into a 16,400 pot when I hit the nuts. Isn't that a pretty terrible way to maximize equity?

Yeah it is. Your turn line is fine imo.

Nuts ( )

Typo. I mean hit my hand.

Fixed: Second Nuts (X)

+1

Did the turn put up a flush draw? It means little but still something imo. I think betting turn for 12k or so is better than your bet. Wouldn't shove turn tho since you're just pricing out sets and two pairs who realize their bad odds (even if you're bluffing a certain % of times) imo.
As played shove river like everybody said.

C-bet the flop in such way that turnshove becomes natural.

open is pretty big
c bet is fine
turn is fine
shove the river youself

The open is pretty big? It's less than 3BBs!