Can I apply for a 30-day extension at immigration if I have overstayed my Visa on Arrival?

Why did you not do it before your entry stamp expired because you lose nothing by applying early and most Immigration Offices allow extensions to be applied for at least 30 days in advance (not Jomtien though)

I am doubtful you have a "Visa On Arrival" (which you buy when you land here, cost 2000 baht and are only for 15 days)

I think you showed up with no visa and got stamped in free stamp (visa exempt) for 60 days.

Be that as it may, to answer your question:

Yes you can apply for your 30 day extension to your 60 day visa exempt entry on overstay.

Good news for you, if your current stamp runs out on a day the immigration office is closed (weekends or holidays) and you go to the immigration office that very next day they're open, you will not be charged the 500 baht a day for overstay and can get your extension like normal.