just label 4 of the guys as part of the factory production team. that's what they are.
Yeah, this is the problem.
Programmers, while from a layman's point of view are "IT", they are not helping to complete to the IT work load. They may help build the business processes, but they aren't pulling cables or tracking down DNS issues. So as far as what they do in IT, it's "zero".
Submitter's description outlines ONE "IT person" in the organization. (him / her)
I would approach this with a two step process; first, get a ticketing system and get all desktop support on it. That will let you show the programmers don't do shit for it, and what the work load is.
THAT sets you up to add other tasks the programmers, the manager, and the subby do on the ticketing, and when the workload is high, just say "sorry, can't do that doing this" and it's all documented.
Then you just do what is important, mark off your hours of the day, and go home. When the shit stays broken and people get pissed about it, they go "why?" and they will see the answer is "not enough people for this." If it's YOUR idea, they won't do it. If it's THEIR idea, they will.
I assume the subby doesn't want to be the person to do the desktop support. So from there, you hire a local goon for a day / evening per week, or a local firm, or some place in India, or whatever. THEY work on the ticket backlog of desktop issues.
Also, you may find that when people have to articulate what is wrong, their problems suddenly go away. People who get help with computers are VERY VERY LAZY and will not learn something. Suddenly rebooting the computer will seem worthwhile compared to (ugh!) writing clear English. Lastly, you can find out which few people are causing the most problems and have evidence to get them to change their ways (or at least stop screwing up their computers). You know, that one guy that always gets the virus of the day (always the same guy, always "i don't know what happened!"), and that one person who's keyboard, monitor, mouse, or whatever needs replacing just because (as a status symbol).