Live hand analysis; $1/3 Bellagio

I am trying to analyze a hand I played last night at the Bellagio. I lost my stack ($125). Based on my analysis below, it seems I should always shove on the flop when facing this situation. Do you all agree?

Hero: Button; KJ (suited diamonds); $125 stack.

Villain: Cut-Off; AQ (suited spades) and $400 stack (approx.)

—Preflop: UTG limped. CO raised to $15 Hero called.
BB called. UTG called.

Total Pot: $61

—Flop: 8h 10d Qs

BB and UTG checked.
CO bet $45 with paired Q (Pot was then $106). Hero called with open ended straight draw (10 J Q K) and backdoor flush draw (diamonds). BB and UTG folded.

Total pot: $151

Analysis: For my call, my equity was 40.61% (per the (Cardplayer.com poker calculator). At the table, I used the rule of four to calculate a 48% equity, based on 12 outs — 8 (open ended draw) + 3 (kings) + 1 (backdoor flush draw).

My pot odds when calling were 45 / 151 ‎ = 0.298. Since 29.8% is lower than 40% (or 48% using rule of four) I made a +EV call.

To expressly calculate EV, we have: (.4061)(106)-(1-.4061)(45)‎ = 16.321. I make $16.321 each time I make this call.

—Turn: 10h

CO bet $100, putting me all in.
Hero called.

Analysis: Before calling, my stack was $65. So I was really facing a bet of $65 into a pot of $151.

My equity, according to the online calculator, was 22.73%. According to rule of two, I calculated 22%, based on 11 outs — 8 (open ended straight draw) + 3 (kings).

My pot odds were 65/(65*2+151)‎ = 0.231. Since 23.1% is slightly higher than 22.73%, I made a slightly -EV call.

The exact EV is: .227*(151+65)-(1-.227)*65‎ = -1.213. So I lose $1.213 each time I make this call.

—River: Blank (maybe 5d or something useless)

Hero missed the draw. Villain turns over AcQc, winning with a pair of queens.

Final question:

What if I had gone all in after seeing the flop and after Villain’s $45 bet?

Pot was $106. I had $110 left.

My equity was still 40.61%.

To calculate EV, we have: p[Villain folds](106) + p[Villain calls][money made from getting called]

=p[fold](106)+(.4061)(106+110)-(1-.4061)*(110)

So this is equivalent to my fold equity plus (.4061)(106+110)-(1-.4061)(110)‎ = 22.389

Although I have no way of knowing my fold equity, it is at least non-zero. Further my EV from getting called ($22.389) is higher than the EV I calculated above from just calling ($16.321) Villain’s flop bet.

Should I always shove in this situation? What could I have done better?