$11 NL HE MTT: Flopped full house - how to get max value?

Hand is from a "Big" MTT on PokerStars. A traditional format with 10 min blinds and even 12 min on the final table. Sadly not so popular these days, so this "Big" only saw around 60 entries. Late registration is around 10 minutes from closing, and around 70% of the remaining players need to go, before we are in the money.

UTG is playing VPIP 67 / PFR 4 over 24 hands, so a typical fish, and not exactly shocking, that someone with these stats chose to limp into the pot. SB is playing VPIP 27 / PFR 18 with a 10% 3-bet over 979 hands, so kind of a bad LAG with a rather high VPIP and a slightly to wide gap between VPIP and PFR.

Obviously the focus here is getting max value, when we flop a huge hand like this, which unfortunately does not happen that often. Decision points:

Flop: Check back as a slowplay or bet for value, and if so which sizing?
Turn: Continue to slowplay by just calling the small bet from SB or raise for value?
River: Small bet or jam for value?

PokerStars, $9.80 + $1.20 - Hold'em No Limit - 100/200 (25 ante) - 7 players
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UTG: 11,238 (56 bb)
MP: 4,314 (22 bb)
MP+1: 9,045 (45 bb)
CO (Hero): 13,292 (66 bb)
BU: 7,080 (35 bb)
SB: 14,384 (72 bb)
BB: 18,836 (94 bb)

Pre-Flop: (475) Hero is CO with 7♠ 7♦
UTG calls 200, 2 players fold, Hero raises to 700, 1 fold, SB calls 600, 1 fold, UTG calls 500

Flop: (2,475) 8♠ 7♥ 8♥ (3 players)
SB checks, UTG checks, Hero checks

Turn: (2,475) 2♠ (3 players)
SB bets 619, UTG calls 619, Hero raises to 3,218, SB calls 2,599, UTG folds

River: (9,530) T♦ (2 players)
SB checks, Hero?

Flop is mostly check V cannot have hit board hard very often we need them to catch up or hero call later streets.

Turn 2s not a card that strengthens most of their range. The question is will we only get this 1 street of big value from the largest portion of their range-draws and weak value leads? Of course if they hit we get more but frequency is what we consider here. LAG leading is good for larger raise as they continue often. The issue is what range are we raising large on this board 3 way. What are we bluffing? Are we attacking a small bet? Will LAG think about that?

River sizing is dependent on LAG range and tendencies. The largest portion of V range is weak hands and the draws they call nothing. If LAG thinks we would attack the small bet turn then they think we can have bluffs. All-in sizing seems the best choice vs that scenario to get the hero call.

If the LAG thinks no one bluffs rivers then we target crying call hands by betting small.