rokaway,
I'm not much of a mechanic, but I've sure done my share of shade tree work, so I'll give you my two cents worth. There are some more knowledgable guys on here that I'm sure will respond with some good advice.
It really sounds like a fuel problem for sure. The new fuel pump eliminated one prospective problem. From the one-hour time frame, it sounds like heat may be a factor. Does a fuel line run too close to a muffler or other heat source, causing a vapor lock?
Another issue ( with its age) may be a clogged strainer in the fuel tank. When the mower sits a while, the stuff clogging the strainer may dissolve away from it a little, but after an hour run time, it has accumulated back on the strainer.
And one other problem is that a fuel line may be collapsing and shutting off the fuel flow, but it looks like you would have already seen that.
Also, it sounds like the injectors are NOT the problem because of the one hour of good performance. If they were clogged, it would run poorly all the time.
I'm sure you'll find the problem. I'll keep checking back.