In all this discussion, you still haven't hit on the right information to tell which model it is. All the numbers you posted, except for the H4--- number form the magneto are part numbers. The fact it has a magneto suggests something well prior to '52. I believe the block part number is for a Super A. Super A's were always available either with or without hydraulics.
Here are some items to check:
Bell housing: large flat top for the Touch Control to mount,
Final drives/drawbar: drawbar mounts on each side with 2 same-sized studs, not a large bolt plus a smaller capscrew,
Instument panel: covers whole area behind battery with steering shaft mount out the top of it, not a small box bolted to the steering support.
A Super A will have ALL these characteristics and an A will have none.
By the way, I have a very late B (215,000+ serial) and it does not have a Super A block.