Another thing to check is your carburetor's choke mechanism. It may be stuck open or not closing sufficiently.
The choke plate reduces air intake, creating the richer fuel mixture necessary for starting an engine. Pumping the accelerator pedal pours raw fuel into the intake manifold, partially offsetting a lean mixture.
Your fuel pump appears to be working. Pumping the pedal for "5 to 10 minutes" would drain the carburetor bowl. If the fuel pump isn't replacing what you've drawn through pumping the pedal, you'd wind up with no fuel in the carburetor. (Too much raw fuel in the intake manifold is what constitutes flooding.)
There is a stepped cam on the choke linkage that prevents the choke plate from closing completely. Flooring the accelerator pedal once before starting releases the cam, allowing the choke to close more completely.
This is why accepted big block starting procedure was to first press the accelerator pedal quickly all the way to the floor and release it completely. Then, press the pedal gently to half throttle and hold there while turning the ignition key to the START position. On an up-to-snuff big block (and most other engines), the result is a near-instantaneous start.
So, first check to see if the choke plate (located immediately under the air cleaner) is closing when the engine is cold. Report back on what you find. (There's lots of variations in choke mechanisms, plus previous owners love to mess with it, so I won't go further until you report back ... and a picture of your choke mechanism would be helpful.)
