ISame thing here. I gave up on fitted sheets. I've tried safety pins as a quick fix. Those are dangerous. If you turn around in bed and it dislodges, the pin could fly off, landing, pin side out, anywhere.

What I do is get some comforters that are larger than the mattress, and layer them on it. When I know no one will be coming by, I save time by just sleeping on the mattress alone.

Now, the obvious question is this: if you live in Oz, why not just have the Wizard fix it?

Absolutely nothing wrong with using two flat sheets, one tucked under the mattress and one over. Sheets are made with a depth of mattress in mind, and yours may be too thick for the sheet. I know, that's aggravating.

That's easy.
If you own a needle, thread, and piece of elastic (you can borrow both from a woman, or buy one of those tiny sewing travel kits they sell at most stores) you can add a loop to one or more of the sheet corners, to anchor it while pulling the sheet to fit over the other corners.

An easier solution, If you can find them; there are sheet straps you can clip onto the sheet corners to anchor it under the mattress.

Get some safety pins like you use with nappies and pin each corner underneath. I've never had that problem myself but common sense after laughing my socks off got me thinking about that idea. so you live on scummy sheets unless you may get women in bed? this isn't a joke, is it? get in the sink and have a very small bath while you're at it.

Get a new bed, perhaps ?

Try doing one corner then the opposite diagonal corner then the last two corners. If that doesn't work, you may need sheet straps that clip your sheets down underneath the mattress.