Dying from oil starvation usually means the engine is totally fried. A shop will easily charge $800+ for a swap or rebuild. Before you scrap it, take a good look at your mower deck. If the shell is solid, you can just buy a used engine online and bolt it on yourself. But if the deck is trashed...
That double jump on the lower valve is a classic sign of a sticking valve or a worn cam lobe. Given the sudden power loss, I'd bet on a valve not sealing. Check your lash and look for carbon buildup. This guide explains how valve issues cause power loss...
Oof. $875 is a bargain with bent spindles, a missing deck chunk, and a blown head gasket. You're basically resurrecting a 12-year-old mower. Hope she appreciates it.