You will need to pull that mane. Button braids will suit her just nicely and are a much neater look than a running braid anyway. All trimmed up - feather, whiskers, beard, ears - and tidy.
Also, get started training that mane to the other side. The mane should be on the off side. Best way to train it is to pull it over to the side you want it on, then braid it (but don't roll them, just tie them off with braiding elastic), making sure the braids sit flat against the side of her neck. Take them out after 7 days, brush out her mane, then put them back in.
Your braids will be much tidier and will look much better if her mane is properly trained before you braid for the show.
edit; just wanted to say that's the best neck I have ever seen on an ASH cross.