If they've introduced these rules it will be because it wasn't financially viable the way it was. Ime prices in social clubs tend to be higher because they can't access the kind of volume discounts businesses can and have a harder time covering their costs due to their income base. May not be the case here, but an observation.
I do appreciate the predicament you're in with your budget and I didn't mean that you would intentionally be expecting them to sub you, but if they can't cover their costs then that is the effect.
I would try putting forward some kind of proposal that gives something that will be attractive to them as well as being easier to you, rather than simply asking for reductions or changes that benefit you. Be creative. Offer them something even if all you're actually doing is reiterating what they get out of it.
Effect is the same if they agree but psychologically the former may be better received. Simply asking them to waive fees in exchange for nothing is not very appealing. Humans are loss averse and people tend to be more accommodating when they feel they benefit from agreeing rather than simply yielding to requests for discounts or whatever iyswim.
So instead of an isolated question of "can you waive the corkage?" for instance, winding back a bit and setting out in more of a format like "we will do xyz, which will enable you to (verify how much alcohol we are bringing, ensure the bar is only opened for the right number of hours...), we would be grateful if you would then do abc, which will..."
Obviously quite how you word it will depend on specifics of situation and how the discussions are going, but I find I get more success when I propose things more as a sales pitch about how the other side is going to benefit even though I'm actually asking them to agree something for me that I need!
It doesn't hurt to say something like "we are disappointed that your policies have changed since our original verbal agreement, but we want to work with you to reach an agreement that works for us both..." but stay calm and try not to trigger them to go on the defensive.
I hope you manage to reach a resolution.