NL25 AKs - TPTK in 3b pot - jam river?

NL Holdem 0.25(BB)
HERO ($28.77)
SB ($28.66) [VPIP: 0% | PFR: 0% | AGG: 0% | Hands: 8]
BB ($39.42) [VPIP: 28.6% | PFR: 28.6% | AGG: 66.7% | Flop Agg: 100% | Turn Agg: 100% | River Agg: 0% | 3Bet: 0% | 4Bet: 0% | Hands: 7]
UTG ($25) [VPIP: 6.3% | PFR: 6.3% | AGG: 100% | Hands: 16]
HJ ($41.29) [VPIP: 42.9% | PFR: 28.6% | AGG: 33.3% | Hands: 14]
CO ($91.48) [VPIP: 28.6% | PFR: 23.8% | AGG: 28.6% | Hands: 21]

Dealt to Hero: A♥ K♥

UTG Folds, HJ Folds, CO Raises To $0.50, HERO Raises To $1.80, SB Folds, BB Raises To $5.60, CO Folds, HERO Calls $3.80

Hero SPR on Flop: [1.96 effective]
Flop ($11.80): 3♦ A♠ 8♦
BB Bets $2.95 (Rem. Stack: $30.87), HERO Calls $2.95 (Rem. Stack: $20.22)

Turn ($17.70): 3♦ A♠ 8♦ Q♥
BB Bets $5.40 (Rem. Stack: $25.47), HERO Calls $5.40 (Rem. Stack: $14.82)

River ($28.50): 3♦ A♠ 8♦ Q♥ 6♠
BB Checks, HERO ? ? ?

Cold 4b always looks scary, I could have jammed this, but since popular hands to do that are AQ and KQ, I thought it might be good to flat, cause I have them dominated.

Turn: of course a Q as usual, I lose against AA/QQ/AQ, split with AK and beat KQ/AJ.
River: complete blank, FD has missed - any point in jamming here for 60 bb? Can we hope to get called by worse? If he slowplays AA here and jams QQ, then this is how it looks like:

Equity Win Tie
MP2 37.50% 18.75% 18.75% AhKh
MP3 62.50% 43.75% 18.75% AA, AQs+, KQs, AQo+

I would have called the shove, but I am just not sure we will get called by worse often enough to justify the jam.