I don't think leaflet drops are a good idea... caring people will eventually find out about rescues and random drops advertise you to possibly the wrong sort of person. (I speak from experience after getting horrid phone calls requesting certain types of massage after I leaflet dropped when I was doing reflexology
)
I don't think that's always the case though, having worked in petshops and been the resident 'animal lady' in my office job I've had the "Small animal rescues exist? I thought it was just cats and dogs" thing loads of times.
I know it's sort of jumping into an unknown area, rehoming to total strangers, but if you stick in the same area too long then there'll only be so many homes you can home to - look at how many people on RU are already at their maximum capicity. You may find some reals jems of an owner out there. For example, I made friends with someone who managed one of the petshops I used to work at, turned out she owned rats like me - and her rats were absolutely spoilt, huge cage, good diet, used the same vets as me etc so couldn't fault her, but she has no internet at home so isn't on any forums. Does that make her less of an owner? She also didn't know of any local rescues to adopt from - there are none immediately near us but a few who advertise online that are close enough to travel to.
Yes, you may get more animals dumped on you but you may home more animals too, and those animals likely would've been dumped elsewhere anyway.
As for cost, this could possible be reduced (or maybe even done for free) by speaking to a local printing company and seeing if they can do some flyers in exchange for having an advertisement for their company somewhere on the flyer? Then it's free advertising for them and they're seen to be helping out a good cause
Or even local members printing out small batches, as many as they can afford to spare ink for - this may help widen the area you can hand them out in too if the members are happy to drop them around. Easier for 5 people to hand out 50 flyers than one person!
You could even try appealing to existing owners by having basic care info on there? Maybe rabbit-savvy vet numbers (they may contribute to costs for some cheap advertising?), handy tips like how to stop water bottles freezing, prevent flystrike, why buns should be neutered or spayed etc and advertise your bonding services to those with lone buns (a chance to educate them face-to-face there too)