William Munns wrote
Hi,
but I plan to lift the car with a chain block at each end, so
there should be no load in either of these directions.

So is there anything inheriently wrong with my plan?

Yes

What thickness of wood should I be looking for to support 1/2
ton, centrally from a 10' span?

Forget wood, use steel box section.

Seek out a steel fabricator if you can't MIG weld.

HTH

Paul.