TDC on the exhaust stroke is 180 degrees off from the compression stroke. Your engine would never start.
Uh, I get the "your engine would never start" thing, but I think your geometry is off.
In a 4-cycle engine, the piston is going to be TDC twice during one cycle. Once on the exhaust stroke and once on the compression/firing stroke. In that sense, you wouldn't be 180 degrees "off" you'd be 360 degrees "off," right? You need two complete 360 degree rotations to complete one cycle.
Cycle 1 - firing/downstroke
Cycle 2 - exhaust valve opens, piston moves upstroke
Cycle 3 - intake valve opens, piston moves downstroke, filling chamber with fuel mixture
Cycle 4 - piston moves upstroke, compressing the mixture