A simple option would be to put a note in each letter box asking if anyone would be interested to sell. Obviously that only gets to the resident owners but it is harmless and a start.
[BTW. I can understand the reluctance of the executive committee to hand over the strata roll with everybody’s contact details even though there is an argument that you are entitled to inspect it. We have had owners intent on mischief that I would not like to give the strata roll to. When they wanted to inform owners about the dastardly activities of the EC we said they could do so by providing their material to the managing agent to mail out.]
So, I suggest you provide a letter that you would like to have sent to all owners and offer to pay the costs of having the strata manager mail it out to all owners (or just the non-resident owners if you have done the letter box drop already). The strata manager and EC should be able to see your letter is innocent and innocuous. It would be much easier to request that once you are actually an owner, not just a prospective owner. IE a member of the club rather than someone from outside the club wanting to advertise.
Where I am it is not unusual for people to ask around to see who has a spare carport space that might be rented. Sale is not an option in our case because they are linked to the units’ title. I rented my neighbour’s second parking space for a year while I working to get one car drivable before then selling the other car.