You will want to be careful about putting in too much MA at one time, you need to be certain that the amount you add will not drive the pH too low as that can damage the pool and equipment, possibly creating stains also.
My understanding of the mechanics (someone will correct this if it is too far wrong) is that the MA first lowers the pH, this consumes some TA, then the pH slowly rises due to aeration which drives off some gases in solution leaving TA where it lowered to.
In general, just use enough MA to get the pH into the proper range. pH 7.5 is the pH of the eye so you want to be near that for comfort and safety when swimming. Therefore the range is something like 7.2 to 7.8. When pH gets to 7.8, use just enough MA to get it back to 7.2 then wait, as long as your TA is high the pH will tend to rise. The more you lower the pH, the more TA gets worn away, eventually it will lower. I you are not trying to lower TA then you just adjust the pH to 7.5 not 7.2.
In our parts of the country, where fill water has high TA (mine is 340) I always have to add some MA on a varying schedule. Evaporation or splash out makes me have to add water, TA goes up, pH goes up, I add MA, pH goes down, TA drifts down eventually, then I have to add water again. I guess if I had to empty the pool and start all over with tap water at TA 340 I might be aggressive about trying to lower the TA using the acid & aeration method. I have done that in the past, but I have developed POP (Pool Owner Patience) and so now I just add MA as needed and track the TA weekly.
I believe that rain will have very low if not zero TA (barring alkaline dust storms?) and so heavy rains will tend to lower TA through dilution but only if there is a LOT of rain. 2" is not a lot, but 30" over the course of a wet winter may be to the extent that this is in excess of evaporation replacement. In the short term, rain tends to raise pH via aeration. So, I guess if you knew a big rain storm was coming, you could lower the pH to 7.2 then let the free aeration and dilution both work to lower the TA as pH rises naturally.
Overall, my take on rain is that in the short term, in small amounts like a few inches, rain is of no matter but for debris and possible dirt in the pool. AGP won't have the dirt from landscaping falling in, so only blown in leaves to worry about. Aeration from raindrops will tend to raise pH some amount, probably trivial but perhaps noticeable. Dilution effects would require a lot of rain combined with overflow from the pool.