KK - 4-way on drawy board

Today a difficult spot with KK. I was kind of card dead on this table and so my image at that moment was probably very tight. I got KK and opened on the CO and got 3 callers behind. The flop is one, you don't like to see in a 4-way pot. On to the hand:

EverestPoker Game #1944569830: Table Bamako-0 - $2.00/$4.00 - No Limit Hold'em - 10:39:32 - 2007/08/16
Seat 1: KvGalen ($653.16)
Seat 2: bifffeno ($1,256.25)
Seat 3: BldZwtTrn ($388.00)
Seat 4: immortal8 ($912.50) -> 26/19/4
Seat 5: dane76 ($403.95) -> 50/15/2
Seat 6: petros66 ($368.88)
dane76 posts the small blind of $2.00
petros66 posts the big blind of $4.00
The button is in seat #4
*** HOLE CARDS ***
Dealt to BldZwtTrn[Kd Kc]
KvGalen folds
bifffeno folds
BldZwtTrn raises to $14.00
immortal8 calls $14.00
dane76 calls $12.00
petros66 calls $10.00
*** FLOP *** [7c Tc 8d]
dane76 checks
petros66 checks
BldZwtTrn bets $40.00
Obviously I have to bet here and I make it $40 which is kind of low, this should have been $50 I think because the pot is $56 here and the board is as drawy as possible.
immortal8 calls $40.00
He instantly calls my bet. This makes me think he has a mediocre hand (AT) or a drawy hand (9/XdXd).
dane76 calls $40.00
This is a guy who will call with any draw/any pair here probably
petros66 folds
*** TURN *** [7c Tc 8d] [4d]
dane76 checks
BldZwtTrn checks
The turn makes one straightdraw (unlikely one) complete and adds another flushdraw to the board. My position is kind of crap here though.
I decide to check and raise (shove) when Immortal bets, as he is agressive enough to make a bet here on the button.
immortal8 checks
*** RIVER *** [7c Tc 8d 4d] [7d]
dane76 checks
BldZwtTrn checks
This river card is good card for me although it completed a backdoor flush draw (which is unlikely here). So I'm about 90% sure I have the best hand here, but I'm not sure if betting is the best option here. I still think both players have a flushdraw/9 or a Tx hand.
Instead of checking I could also make a 'fake' blocking bet here, hoping for a raise, but that's kind of tricky with the backdoor flush and paired board. Another option is a normal value bet that hopefully gets pair by a Tx hand. I chose to check, but the hand was checked out.
immortal8 checks
*** SHOW DOWN ***
dane76 shows [9h Qc]
BldZwtTrn shows [Kd Kc]
immortal8 shows [Jd Qs]
*** SUMMARY ***
Board: [7c Tc 8d 4d 7d]
BldZwtTrn collects $173.00