This has been pointed out to you by many posters, including myself. You've rejected every technical treatment of the subject and started as an a priori assumption that 'with proper position sizing it's impossible to blow up.' It has been pointed out that so long as your wealth and life span is finite, this is not true even if the stock market is well behaved. In fact, analysis of martingale systems explicitly shows that this is true. Yet, you start hang on to your misconceptions.
Martingale (or, let's call it "averaging down" since I guess technically I'm not "martingaling") systems won't blow up with proper entry points. How is this not clear? If you're averaging down on a tight range, then yes, you'll blow your account once price goes one tick too far. Lots of noobs do this. I've done it in demo accounts. I never said this wasn't possible, in fact, I said that it was possible, and I'm saying again, yes, it's possible, and yes, you're right, on those crazy 3, 4, 5 sigma days, yes, you will blow your account.
You keep saying this - despite it's been shown to you for not being true; So long as the entries are fair (otherwise, your entries have 'edge', which you keep saying you don't), you will blow up any account with some probability assuming you don't have infinite account size. This is a fairly standard result in probabilities theory. It's been linked to you and explained to you. Yet, you keep going back to your a priori assumption that such systems "won't blow up". So you either believe you have some edge (ie, you have better than random entry points; you believe the market will go up under some time frame), or you keep insisting on something that is simply not true. There lies everyone's frustration.
OK, I'll help you. I have actually done the calculations once (just for fun). If you do what you have suggested with 2 STD OTM long options you have a shot there. The non-linearity of the payoffs are potentially suitable for the exponential averaging. However, it only works when the theta is not too harsh on you.
Again, if you do it in too narrow of a range, then yes, you'll blow your account. I'm not disagreeing with that. In other words, if you're doing this on SPY and you make your last entry when SPY hits 100, then you're probably going to eventually run out of money before you make any money. Or if you're doing it on the ES with a $10k account and you're buying more contracts every 5 or 10 points against you, then yes, you're going to eventually blow your account. Sounds interesting. I don't know anything about options, tho. What is theta?