There are multiple options you can try. First and probably the most convenient is to attempt introducing an enclosed litter box. You're right that most cats don't prefer it and some may even refuse to use it. That's why it's best to give your cat the option. Start by having the most open boxed litter boxes you can have and then ideally just introduce only a single enclosed litter box. If it works and your cats use it, then in order to follow the 2+1 rule, introduce 2 of these boxes (but I'd still keep one conventional litter box to give your cats the option and to make them happier).
Another option it to try putting boxes in unconventional places like you said. In my experience cats are usually not picky about where to use the litter box and will still go there. However, I'd recommend not putting the boxes on high places like the refrigerator as you suggested. In a tiny place, it is vital they still have as much free spaces as possible to play in or wander and for cats, that especially includes vertical space. And if its possible for them to go up high on the refrigerator, that is an excellent place for them to hang out and no cat's gonna wanna just hang out up there if it's also where everyone else is going to the bathroom. Another possibility is that you mentioned putting boxes in places like under the bathroom sink. That is technically an enclosed space that is just larger than an enclosed litterbox would be. You could try putting boxes in there and then SLOWLY transition to an enclosed box by having typical litter box there for couple weeks, then putting in an enclosed box (in the exact spot) for a couple more weeks and then moving that box to a more convenient location. However, I'd recommend not moving litter boxes around for a while after the move, so that your cats have time to settle and really get to know and be comfortable in the new place (since cats really HATE change).
A final option I can give is like a compromise between you and your cats and comes with potentially the most problems and requires the most work. But despite the 2+1 rule (which I do now follow), I have had multiple cats that are perfectly happy using less number of litter boxes, so it is possible to do so. However, I will point out these cats were using that few amount of litter boxes from the moment I got them as kittens and so were probably used to it by then. This has led me to believe though that the 2+1 rule is less about territory and more about hygiene. So you could start off with fewer boxes (I'd personally to give your cats time to adjust to the change, start by taking only one litter box out and then in like the option above, once you see your cats are alright with that, take out another one weeks/months after the first reduction). Of course, be prepared that since your cats are adults with established routines, they might not be able to make this adjustment or at least not make it easily, so I'd be on the lookout for cat pee or poop in inappropriate places (any inappropriate elimination should be cleaned immediately and thoroughly to get rid of smell, and ideally not with scented cleaners). But now for the hard work on your part. To make this adjustment go as well as possible, the litter box should at the very least be cleaned DAILY. But if using only one litter box for two cats, it is possible that it should be cleaned even more frequently. So before your cats pees on the floor and you throw in the towel, just clean it up well and adjust how frequently you clean it. If, however, you're cleaning it as frequently as you possibly can and the inappropriate elimination is still happening, then that's when I'd say you should give up this method and try something else. Don't be discouraged though when I warn against possibly peeing outside the litter box: it's only a POSSIBILITY. I don't know your cats and they may be perfectly happy to make this change. Its worth at least trying this and if you decide you can't take it, then after the first pee outside litter box, then you can decide to try something else (but it's still worth at least an attempt!).
I'd like to make a final note on a balcony litter box that you mentioned. I'd think that's a wonderful first idea to start with. Its not really enclosed and its out of the way but also in a place that you're cats will go. The worst possible scenario is that it becomes a summer-only litterbox but it still is an added option your cats can use and I do believe they will have no problem using it. However, if they do refuse to use it in winter when its cold, then I'd recommend still keeping it out (as an option), but using the methods stated above to add the appropriate amount of litter boxes in the house for them to use (you can never have too many litter boxes). Alternatively if you still find you cannot have 2+1 litterboxes in the house, then use the method stated above to properly introduce them to a reduced number of boxes in the house.