Looks like people have sorted this one out. Here are some general thoughts about this type of problem:
When the person in the cemetery office doesn't find the person you are looking for, they will next go to their index card files, which is what they used before computers. Some cemeteries have thrown these away. Some still have them.
The really diligent ones will pull out the grave map of the section where you think the person is buried (if you know it) and pore over the map to see if they can find the person. (If the Mount Carmel person spent 20 minutes, they probably did this.) You may have to specifically ask them to pull out the map and look.
Most of the burial societies in New York cemeteries buried people sequentially. So the person on either side of a particular grave is the last and the next person to die, unless the family chose to buy two plots together when the first to die was buried. Some societies bury men on one side and women on the other.
All this is to say that looking at who is buried nearby may not be helpful if the spouse you are looking for died a good number of years before or after.
Kudos to A.E. Jordan for using the cemetery's online database to sort this out. Luckily, Mount Carmel's locator page is one that allows you to enter the society name. Otherwise you would have to scour all entries for the year of death.
All of the cemetery websites for New York City Jewish cemeteries seem to use the same back-end software. So, be aware that those pages that allow you to enter a society name in the search data have a flaw which will not allow you to enter two words. In our example, where our person is buried in a society called VEREIN CHOROSTKOWER, if you enter VEREIN CHOROSTKOWER as the society, the website software removes the space, makes it vereinchorostkower, and comes back with no results. If you enter just VEREIN, you will get results for all societies that include VEREIN in the name (this will bring up Leah, Brown and others). If you enter just CHOROSTKOWER, you will get results that apply only to VEREIN CHOROSTKOWER. Entering year: 1930 and Society: CHOROSTKOWER (and nothing else) brings up only 4 results, including LEAH, BROWN.