backtesting software

I understand that it would be very difficult to accurately backtest all factors/contexts and in the moment intuition...

I would not say it is difficult but impossible. 

nonetheless I have a desire to at least do some form of backtesting.

Al somehow does in the EMINI, check the daily setups section.

So, before I go spend a ton of time and money on various backtesting software, or a ton of time and money developing my own backtesting software, does anyone have any recommendations?

Save your money and don't waste your time, you will need both if you want to be succesful with PA... it takes years to learn.

This would specifically be for backtesting intraday price action strategies (you know... like strong breakout candle or a wedge reversal,

For you to backtest, you need to assign a probability for every single setup and this depends on the context. You are here precisely to learn that so you don't know as for today the correct parameters to do the backtest. And once you know, you won't need to backtest anymore.

I'm not sure how assigning a probability for every setup is related to backtesting, it would be more about defining the criteria for entry/exit and then running it.  But I do understand that it is very very difficult to construct a mechanical system that backtests well and continues to work in the future (though clearly not impossible if teams of PhDs at institutions can do it)... this is more about generating or simply validating guidelines or rules of thumb.  For example, Al quotes statistics in his book, such as if the day's range is half of an average daily range, then whatever percent of time (60?) you'll get a breakout and doubling of the range.  It is things like this that would be nice to go and confirm.  And it is also nice to see if it is something that happened with a very high probability from say 2000-2010, and then happened at a very low probability from 2010-2022... it is important to see if the events are distributed somewhat evenly/randomly over time or if it is something that used to work and now no longer works.

Or something as simple as getting the frequency/odds of 2...3...4...5...etc bull candles in a row.  A lot of this stuff becomes intuitive after looking at the charts daily for years, but just gives me a warm fuzzy to have some data to backup any assertions I may have.

Does anyone know what Al uses to get the statistics he states in his books/courses?

I'm not sure how assigning a probability for every setup is related to backtesting, it would be more about defining the criteria for entry/exit and then running it.

But for you to define the criteria you need to know the context. A strong bull bar is at the same time a breakout (high probability the MKT keeps going in the same direction) and a  climax (high probability the MKT reverses the direction). The context informs which one is more likely. If you test without discrminating if a strong bar is a breakout or a climax, your results  will be mixed and tell nothing. Same thing with all the setups.

Maybe this example will be easier to see: a H2 at EMA. This is said to be one of the best  setups but when before the H2 there is a climax that effectively reverses the trend (even tho still making higher highs and lows) you can't expect the H2 to work. In fact, if there are some other elements in place you have to expect that it fails and actually you have to sell it. Again, if you backtest if H2 at EMA works, your results will be wrong because you will be mixing withtrend H2 at EMA with countertrend H2 at EMA.

though clearly not impossible if teams of PhDs at institutions can do it

I really don't know, you might be right but you don't have a team of PhDs and also they might be using other systems than PA (indicators, statistics, etc.) I seriously doubt PA can be programmed. This is our real edge!

And it is also nice to see if it is something that happened with a very high probability from say 2000-2010, and then happened at a very low probability from 2010-2022... it is important to see if the events are distributed somewhat evenly/randomly over time or if it is something that used to work and now no longer works.

One of PA tenets: it worked, it works and it will keep working until we evolve into a new species. I hope it is right 😉

A lot of this stuff becomes intuitive after looking at the charts daily for years, but just gives me a warm fuzzy to have some data to backup any assertions I may have.

I fully understand what you mean, and I couldn't agree more in general but, in this particular case, it doesn't work because while you are trying to backtest, your trading skills (PA reading and placing trades), which are what ultimately will give you the money, are not developed. 

Does anyone know what Al uses to get the statistics he states in his books/courses?

Experience.

I will not continue, I think you get my point but nonetheless, I want to repeat that your approach is great, testing before comitting, but the effort needed to test here might be bigger than the effort needed to learn, and that makes it not worthwile!