I am happy to assist with organising Cruiser.
Many restaurants will be open to negotiation of BYO (and a blanket corkage charge) with larger groups or wine tastings. Obviously there are also liquor licencing requirements, as some restaurants don't have a BYO licence, so need a temporary exemption (to do it "by the book").
Slightly OT: The City Wine Shop actually ran a Champagne experience a year or two ago. The price was quite high. I couldn't go due to travel, but some friends went and thoroughly enjoyed it. Interestingly the "Tea Room" at Melbourne Supper Club would be an excellent venue for a private dinner and wine tasting, however it is likely that particular business would prefer that you tasted their wines (to sell to you), rather than your own.
I can think of one or two candidate restaurants in Melbourne and Albert Park.
I am happy to assist also.
FWIW: All restaurants with a license to serve alcohol are BYO - although many choose to refuse it as it cuts into their margins. A delicate touch, methinks.
And now I have forgotten the third thing I was going to say!
Edit: I remembered! Should this be split off into a separate thread to keep the discussion about champagne on track?