Ok, here's the deal:
What is considered as a standard for transliterating Ancient Greek is the so-called
beta code. It uses an asterisk (*) in front of a character to indicate a capital letter. So, both W and w map to ω, while *W and *w map to Ω. In addition, if the character is supposed to be a capital, the order of the accent symbols also changes. while ὠ is W), Ὠ is *)W.

I also noticed that if you search for *dias, goldendict ignores the asterisk in the beginning, and brings up results for dias. Anyway, it is quite confusing and I don't know if you have any better suggestions, but I thought that since capitalization will be ignored most of the time anyway, I might just as well map everything to lower case.
I did think about creating two different files, one for ancient and one for modern greek, where the file for modern greek would include proper capitalization. But then I think that would confuse many users. And goldendict gives case insensitive results anyway.
I have to admit that in my testing I would often get "No results found" when I searched for words with a lot of accent symbols, but the correct word would usually appear as the first suggestion offered. Which I guess is pretty good when one has to use four letter combinations to get one vowel.