I’ve got 10 bikes and although I have tonnes of space for them in my workshop, which is about the same size as the house, I don’t want to waste space storing largely inanimate objects, even if they are quite pretty to look at. Less room for tools and other toys etc.
So I’ve tried a few solutions and concluded that the best way of storing a bike, using the least amount of space is to get some of those front wheel bike hooks that eBay have for a few quid each and to mount them as high as possible. I quickly learned that because of the width of modern bars, 10 bikes takes up a lot of wall space, so what I then did was to remove the front wheels, turn the bars and hang the bikes from their maxles instead. This allowed me to move the hooks to within about 15 inches of each other. I then bought some large S-hooks, also via eBay, which can be hung off the headtube, with the front wheel then hung from there. So the wheels don’t cause problems. Removing pedals would make things easier, but is obviously more of a pain.
The above gets the bikes in half the space and lets you mount them higher up too. My hooks are 2.2m up, so I have space under the bikes to make a storage chest type thing to fill with biking kit, helmets etc, that can wheel out with a work-stand attached. Long-term I might investigate a winched platform to lift all the bikes up into the vaulted roof space instead, but this is a good compromise at the moment.
If you have a bit of space or some high ceilings then that could be your best bet. Two deep screw holes with decent plugs and screws to attach a batton to the wall, then the hooks screwed to the batton. I know you say no holes, but you won’t get caught and a bit of filler when you leave will sort it out easy enough. Or you could put a decorative edge on the batton, paint it to match the wall and your landlord likely wouldn’t even notice it if you left the wood in place.
Do you have a loft space at all? You could fit a winch perhaps to allow you to easily lift the bikes up and down.