Wow. Those birds are like a feathered Punnet square.

"Half-goth babies."

Is there some sort of time-related communication from the repairperson or property manager you could at least hold over their head and rant about?

Fortunately, the property manager arrived about half an hour ago with the repairman in tow, he tried to light the oven and confirmed my description of the problem, he took our oven apart and I took the opportunity to clean various bits of it while they were dismembered, and he put it back together having identified the issue, which will require a new part to fix. So we still can't use our oven, but at least we can use our stovetop, and that is better than nothing in the meantime.