That does appear to be about 1-1/8", yes, but the problem is that they don't make a winged shoe in that size. In your case, 1" and 1-3/32" are the standard options.
We do sell the 15-001, which is 1-1/8", but it lacks those wings, which help keep the balance aligned in the track (if needed).
I suppose you could go with the Series 395 channel balance. This has a 19-005 top and 15-001 bottom, but considering your old shoe has wings I'm hesitant to recommend that. Like I said before, if the shoe ends up being too deep then what will happen is they'll dig into the vinyl channel as you open and close the window, causing irreparable damage.
As for the problem you're describing, the fact that the balance isn't being lowered with the sash when you close it is definitely a problem, but that doesn't have anything to do with the shoe. The only function the bottom shoe does is keep the balance stable; it does not interact with or catch on the sash in any way.
It almost sounds like the top sash guide might be broken. These are located in the top two corners of the sash and they're what keeps the balance in the sash during operation. You may want to check to ensure yours are still in good condition; when the top sash guide breaks, there's nothing to hold the balance to the sash.