Apply for SNAP anyway. The requirements are purposefully hard to understand because that creates a barrier that discourages people from applying, which saves money. If you get denied, whatever, but if you don't apply you won't even see what you are eligible for. And there are several ways to meet the work requirements beyond just working a regular job. Having an active SNAP case, even if your allotment is $0 a month, will give you an active case number which can be used for income verification for other programs like free phone service.

For disability, count in getting denied the first time. Generally that's standard practice, and you may need more than one appeal, but if your wife is unable to work she will eventually get approval as long as she keeps her doctor's appointments and gets everything documented. Don't mess around and smile or say something like "fine" if one of those doctors asks how you're doing--they will write it down and it will go in your file which will look like the doctor thinks you are without pain. There is also Vocational Rehabilitation which helps people with disabilities get jobs and accommodations so they can do their job comfortably. Good luck.