Hi Ethan, nice little thing!
as usual with pyrenomycetes, a first critical step is to assess whether asci are uni-or bitunicate.
I say critical because it is often not easy to clearly assess.
IKI is not diagnostic but Congo red or coloured inks may be useful to understand the ascus apex anatomy.Judging from your photos the apex is not thickened but appears to be topped by a ring-like structure that would possibly stain in Congo red, heated if necessary.
If positive, this reaction would strongly suggest Sordariomycetes rather than  Dothideomycetes and I suggest you to look into Thyridium, there is a recent paper by Sugita & Tanaka doi: 10.3897/mycokeys.86.78989 which might helpful.

All my best,
Jacques

Hi Ethan,
thanks for your excellent images.They indeed show an apical ring like structure, refractive, unstained in CR but contrasting against the pale red ascus scontent. 
Positive or negative stain in CR is abviously an informative feature, in connection with the chemical nature of  the ring. And it supports the lead toward Thiridium and not toward Dothideomycetes. Apical rings do occur in a few genera (like Delitschia for example) of the latter class but uncorrelated with the other features of your collection.
Good luck!
Jacques