Sometimes what "has" to be done just can't be done, and this looks like one of those times, so there is no sense in belaboring the point. So we deal with the facts on the ground. There is not going to be a solution free of compromise so we have to free up our minds to accept some ideas that are not ideally what we want to do.
One possibility is to build the icing platform, maybe use the old mirror trick to make it look like it is longer and bigger, and more or less permanently park your two or three reefers there (the mirror making them look like four or six cars), with more than usual detail showing them actually in the process of being iced -- the platoforms actually going to the open ice hatches with blocks of ice being pushed by workers with pikes in their hands. From an operating standpoint that track would be off limits because it is a scene, not a working siding. I have not seen this done with iced reefers but I have seen it done with stock cars where the animals have been unloaded for the mandatory rest and watering. Those stock cars do not move and the scene can be more detailed as a result.
So what do to about incoming reefers that need to be iced, assuming it is the realistic operation aspect that you seek to replicate? Well you could introduce a deliberately time "wasting" move of the block from one track to another and just declare them to be iced when the movement is done. The point then is to introduce that sense of delay. I know guys who do something like that when declaring that a cut of cars is being run over a track scale -- a scale track that they do not actually model. The point is to force your yard crew to do something so they aren't just sending that cut of cars on its way. This is sort of similar.
You could arrange for the reefer block's arrival to signal the end of any giving operating session with the actual icing taking place during the unmodeled part of the day so the start of the next session sees the cars iced and ready to go.
You could regard your yard as, in part, a "fiddle" yard and take the cars off line by hand so you free up that track, and again just declare that the cars are being iced.
Hard to visualize the situation but combine that first idea -- the scene of permanently parked reefers being iced -- with the cut of actual operating reefers being pushed behind a backdrop behind the icehouse and then pulled out again later. A sort of single-use staging track. Possibly to create room for this the icehouse would be mere building front against a special mid-yard backdrop, even if the actual layout backdrop is further away. Am I making myself clear here?
Dave Nelson