Hi teddy, thanks for your kind words. 
 
I wrote this reply a few months ago and think my game has improved significantly since then. 
When I wrote this post I figured open jamming was +EV and villain's OOP flatting range has pretty good equity against us which we are happy to fold out. 
 
In a single raised pot, we see the flop with 4.0 BB in the pot (P1). 
We will have (S - P1/2) left behind.
@ 19.0 BB, we see a flop with (19 - 4/2) = 17.0 BB left behind and we can end up playing for a 2 * S = 2 * 19 = 38.0 BB pot. 
Roughly speaking, we're going to need 17 / 38 = 45% equity to stack off on the flop if villain puts us to that decision. 
By considering a flop equity distribution against the range I originally proposed as an estimate of villain's OOP flatting range, we can see we do this about 75% of the time. 
http://www.propokertools.com/simulations/graph_hvr?g=he&h1=Ax3x&h2=KxQx-Kx2x%2CKxQy-Kx5y%2CQxJx-Qx3x%2CQxJy-Qx7y%2CJxTx-Jx6x%2CJxTy-Jx8y%2CTx9y%2CTx8y%2CTx9x-Tx7x%2C9x8x%2C9x7x%2C8x7x%2C7x6x%2C6x5x&s=generic
If we assume that we play well post flop, we can roughly assume that we will be getting all in when we have the correct equity to do so.
Because the flop equity distribution is approximately linear between (0,100) and (75,45) we can calculate the area under the flop equity distribution curve by adding the area of the triangle above 45% equity across 75% of flops to the area of the rectangle up to 45% across 75% of flops.
A = 0.5 * 0.65 * 0.45 + 0.45 * 0.75 = 0.48375
So our average equity across all flop distributions that we have sufficient equity to stack off on can be calculated by A / x, where x is the horizontal range of flops we have enough equity to stack off (75%). 
avg equity = 0.48375 / 0.75 = 0.65 ~ 65% equity
=> our postflop equity is pretty decent and if our opponent plays straight-forwardly (like we expect him to untill he demonstrates otherwise) we expect he will let us know when we're behind.
 
If we play better than villain postflop, upon relfection I don't think we should be too concerned about folding out villain's OOP calling range. In position with our postflop (pot equity, fold equity) across the entire flop distribution we should be able to play Ax3x profitably vs villain's OOP flatting range @ 19.0BB. 
 
I agree with you that we may be able to do a bit better than this by exploring under which conditions a min-raise may have better expectation ...
 
We expect villain will call an open jam with something like [A, KQ, AA-22] against which we have about 40% equity.
http://www.propokertools.com/simulations/count?g=he&h1=Ax3x&h2=A%2C+KQ%2C+AA-22&s=generic
He holds a hand in this range about 19% of the time net of card removal effects. 
*Propokertools PQL:
select count(inRange(villain, "A, KQ, AA-22")) as stackoffrange
from game="holdem", hero="Ax3x", villain="100%"
http://www.propokertools.com/pql
 
EV(open jam) = f * P0 + (1-f) * (2 * S * e - J )
where
P0 = 1.5 BB
f = 0.81
S = 19.0 BB
e = 0.40
J = (S - 0.5) = 19.0 - 0.5 = 18.5 BB
EV(open jam) = 0.81 * 1.5 + 0.19 * (2 * 19.0 * 0.40 - 18.5) = 1.22 - 0.63 = 0.59 BB
or we can think about our expectation as two subcomponents:
fold equity = 1.22 BB
pot equity = -0.63 BB
 
So under what conditions does it become better to min-raise? 
This can be modelled accurately using decision trees but becomes less and less useful the more assumptions we need to make in a readless context.
But we can come up with some simple reference points to consider:
 
1. How often does villain need to fold to a min-raise that we do better than the 0.59 BB from open jamming? ie. pure pre fold equity against villain's fold to min-raise range.
fold equity = f * (P0 + R) - R
let fold equity = 0.59 BB
R = min raise = 1.5 BB
0.59 = f * (1.5 + 1.5) - 1.5
f = 2.09 / 3.0 ~ 70%
=> our pure preflop fold equity (ignoring our pot equity which in this case is rarely awful) from min-raising is worth more than the EV of open jamming if villain plays less than ~ 70% of hands OOP (note this is not terribly useful except against the nittiest of nitfish because we always have pot equity to go with our fold equity preflop). 
 
2. How often does villain need to fold to our cbet in a single raised pot that we do better than the 0.59 BB from open jamming? ie pure flop fold equity vs villain's flat and check to us on flop range.
fold equity = f *( P1 + R ) - R
let fold equity = 0.59 BB
and assume R = 0.5 P1 = 2.0 BB
0.59 = f * (4.0 + 2.0) - 2
f = 2.59 / 6.0 = 43%
=> our pure flop fold equity (ignoring our pot equity which in this case is rarely awful) from min-raising then cbetting is worth more than the EV of open jamming if villain folds to our cbets greater than ~ 43% of the time.
=> given we expect villain to flop well ~ 25% of the time (see above flop equity distribution) and that we expect that villain will play straight forwardly,  there will be a difference of (57 - 25) = 32% betwen the frequency that villain needs to continue vs our flop cbets for our flop fold equity alone to not exceed our expectation of open jamming preflop. When you add in some skill for picking and choosing which flops to cbet based on which flops hit villain's perceived range, an aggressive two street strategy may be even more profitable than these raw frequencies would suggest. 
 
The finding of point 2 is especially relevant vs the passive fish at the micros => a lot of them continue very wide vs opens and then play fit or fold to flop cbets. Meaning we will be capturing basically that entire juicy 32% spread in a larger flop pot from our pure flop fold equity. Add to that, that we very rarely have 0% pot equity and min-raising is looking pretty damn attractive. 
 
Thanks for pointing this out, it's really beneficial for me to look at my thinking has evolved from 3-4 months ago. 
I was being a little too aggressive with rag Ax 15-20BB vs villains who were not 3b bluffing enough preflop and playing so poorly postflop that I was costing myself 2 street expectation for the sake of simplifying my preflop decision. 
 
I tend to agree with you that 15.0BB forms a rough inflection point at which it becomes rarely incorrect to open shove low suited Ax.
=> villains tend to contract their flatting range and expand their 3b jamming range around this point
=> our open shoves get called with a wider range of hands against which we have better pot equity
=> net result is the expectation of open shoving with suited rag Ax increases and the expectation minraising decreases
 
Against the loose passive fish that aren't thinking in terms of effective stacks and just want to see lots of flops then play fit or fold => it might still be better to minraise down to about 10BB? 

I meant to call the 3bet pre, not limp pre. I thought you were talking about jamming vs calling the 3bet, sorry about that.