Hi Mike,
The wooden block was made for a different purpose . I worked on a lot of Explorers when they were in service, at a REME workshop. Not sure where your puller originated from, but to describe the set we had, I guess it was factory supplied, well used anyhow, even the local bus company and garages borrowed it for their demobbed Explorer recovery trucks.
There was a very heavy box spanner which must have been 18" to 24" long, with a bar about 2 or 3 foot long welded at right angles at the end. The wooden block was about 8" square and stood on end to support the end of the box spanner, the top of block was radiused for the spanner to sit into. One person holding the box spanner firmly on to nut and supporting block, other person with sledge hammer welting the end of bar to release nut. Once nut is loose, the puller which looked like a modified hub cap, was bolted on to the hub, the extractor screw had same size hex head as nut, so box spanner was used again to shock the hub off, as you say, a thump on the end of the screw helps once it is loaded.
The hubs should be tight on the taper shaft, else the key is likely to shear and tapers wearing. I recollect having to renew a taper shaft on one occasion, due to a loose hub and damaged keyway, the tonnage to push it out of the gearwheel was terrific, something like over 30t.
Hope this is not a case of teaching grandma to suck eggs, but it all came back to me when I read the thread :-D