You know, there are so many variables in soap making (formulas, methods, molds,environment) that I think we just have to keep experimenting to see what works best for us and try the suggestions of others on the board. I have tried many things over the years.
Here's what I have noticed over the years with my soaping (my workshop is in my finished basement with a couple of grates in the furnace ducts, it rarely gets higher than 69 degrees summer/winter or lower than 55 winter, and the basement is humid so there is a dehumidifier running year-round, also, I allow 99% of my soaps to gel and I use both EOs and FOs):
1. my soaps with essential oils are most likely to ash, especially those that are predominately lavender or predominately patchouli. I've also had issues with soap containing rosemary.
2. I get more ash in the winter, especially when we've been using the wood stove a lot on the main floor, meaning the furnace heat is not getting into the basement so it is at ambient temp of 55-64 with no warm dry air blowing in (I am in the northeast US). I used to use a space heater, but it doesn't seem to make a difference the way the furnace heat does.
3. The majority of my ash is on the tops. In winter, I am more likely to see ash on the sides, with occasional deeper ash into the soap
Things that work for me:
1. reducing my water, except where full water would slow down rapid acceleration/help prevent overheating
2. most of the year I soap cool (slushy oils and cooled lye). In winter I try to use oils and lye a bit warmer
3. if I anticipate ash in a batch, after cutting it to cure I will cover it with paper towels. In summer in my environment I just need to lay the paper towel on top of the bars and it's sufficient. In winter I find that I need to lay it on top and fold the sides down, pressing lightly so the sides stay down (I don't weight it down or anything, it just sits there covering tops and sides, the ends of each row are still exposed to air--I haven't seen a delay in curing time. )
4. I tend to 'frost' the tops of many of my soaps after I pour them. Then, if/when they ash, the ash is part of the frosting and looks like it was intentional. The technique is called 'embrace the ash' lol. Going along with that, if I don't frost them, I sift some silvery mica on top and it incorporates into the ash.
Also I swirl my tops as you have in your photos, and then I lightly frost them--you just have to determine the best time to do this with your batch so the colors stay distinct. Be patient, try different things, and remember that our own eyes are the most critical.