i have been to many greek baptisms - and it's not necessarily YOU that is being shut out - i have been where there has only been a female godparent - but from what i understand, unless there is a very liberal church that is attended, official godparents can, in the eyes of the church, ONLY be Greek. i have been to a number (mum's two best friends are Greek Orthodox) - and it's only in the past few years that a priest (can't remember the exact title in Orthodox church but i think it's priest) at the local Greek Church has said he'd be happy to educate a non orthodox person on becoming godparent.

from the "asking" perspective - i don't believe the parents of the child are supposed to ask! because the expense factor in a greek baptism is so high (as you know, godparents pay for baby outfits - more than one - material or outfit for mum, all the gifts for attendees) - it's supposed to be the parents being honored by someone asking if they can be godparent. this may have changed more recently though.

i don't think they're deliberately excluding YOU - it's just the religios side of things that perhaps dont include you so much kwim? i would be a little wary of the financial viability thing though. it's a decision you and DH (whether you're officially acknowledge as godparent or not) need to discuss. and perhaps you need to discuss with your DH your concerns over being effectively ignored as well - he might be able to come up with ways to include you more...