Gent, you're a hoot. :razz:
"...How do I prevent this from forming in the future? ..."
To recap Irish Lass, she listed these things that can form "ash" of one form or another on soap:
-"...sodium carbonate
-sodium hydroxide
-soap crystals that have separated from the main body of soap
-or some other water-soluble material that gets deposited on the soap...."
Speaking more specifically about ~soda ash~, it forms when water migrating from the interior to the surface of the soap also brings residual lye (NaOH, sodium hydroxide) to the surface. Lye really doesn't like to remain as lye, so a film of excess lye on the soap surface will typically react fairly quickly with carbon dioxide (CO2) in the air to form soda ash (sodium carbonate, Na2CO3). This evaporation and reaction process happens from the time you put the batter in the mold through the initial few weeks after the bars are cut. I saw this process happening dramatically in the two batches of "super lye" soap I made (see the thread about lye-heavy castile that I referenced in my earlier post) -- there is lots of lye and lots of water in these soaps.
Soda ash is most likely to form during saponification in the mold when there is a lot of evaporation and a lot of free lye present. This is why soda ash is often found on the tops of the loaf -- the top is the only place where evaporation and lye migration can occur when the soap is in the mold. More soda ash can form during the first few weeks of cure, when evaporation from the cut bars is highest and small amounts of free lye may still be present in the soap. This is when you'll find soda ash forming on the cut surfaces and sides of the bar.
***
So, okay, Shalisk, you ask how to prevent or at least minimize it? First off, I honestly don't think you can absolutely prevent soda ash from forming. The reaction of NaOH + CO2 --> Na2CO3 is simply a fundamental aspect of the beast we're working with.
One way to minimize ash formation is to reduce evaporation during saponification. Many people lay plastic food wrap directly on the exposed surface of the molded soap. Not sure if a lid on the top of the mold will work quite as well, but it certainly can't hurt. The point here is to eliminate or reduce the amount of air (and thus the CO2) near the soap surface and also to reduce the rate of water evaporation (and thus reduce the rate of lye migration to the soap surface) during saponification. If you can do this successfully, you should be able to reduce soda ash formation.
It's possible that the CPOP method might increase the rate of soda ash formation during saponification, but it's pretty clear to me that avoiding the CPOP method does not keep ash from forming.
You could wrap the soap bars in plastic right after they are cut to prevent evaporation for a few weeks while any traces of residual lye might still remain, then unwrap to allow the soap to dry. This will slow the cure time and possibly create more problems than it solves. I haven't tried this, and I have my doubts about whether this is a good idea, but something to think about.
Dissolve the soda ash so it doesn't appear objectionable. One school of thought is to spray molded soap with high-proof alcohol a few times during saponification. Some swear by this. Others say it doesn't work reliably. Irish Lass quotes Kevin Dunn as saying soda ash is insoluble in alcohol, so my guess is an alcohol spray is not a complete solution to the problem of ash in general. Another approach is to use steam or a bath of warm water to dissolve soda ash on the bars. This is a reliable method, although time consuming and a bit messy.
Plane off the ash. Some people might think this is tantamount to shooting a mouse with an elephant gun, but it certainly works.
Accept the ash as a normal aspect of handcrafted soap.
I, too, have had some really weird ash form at times apart from the norm, but all was benign. 
