There are a lot of errors with your assumptions. I was looking at my Browning BPS 10 gauge and thought the .45 springer would not be any bigger than this---it wears a 30" barrel. Big, yes but not nearly as unwieldy as you have proposed.
I have been running some ideas on paper and in my head about this thing.
First, a steel coil spring is going to be too big and hard to deal with. Taking a page from the PCP world and my Browning BPS, why not make much of the gas (air) spring a reservoir that resides under the barrel. This would give it a lot of volume, which would then be a way to even out the spring force, i.e., making it nearly constant.
Second, given that an efficient spring gun has an efficiency of about 0.4, and our design is going to have a pellet with about 308 ft-lbs, we need a spring energy of 770 ft-lbs. With an adjustable stroke and pressure, we can tune the thing for best efficiency and make a smooth shot cycle. Our gas spring can be run at quite high pressures if needed, even along the lines of PCP pressures, though I don't think we need to go that far. For instance, a bit over a 2--1/4" diameter piston will have four square inches of surface area. A four inch stroke would require 576 psi in our gas piston. A three inch stroke would require 768 psi. The diameter of the piston could be reduced if needed, and increase the gas spring pressure.
Third, if the piston is designed as a hollow tube with a plug, then that gives a greater volume of air for a given stroke length without sacrificing piston area. The stroke length can be adjustable in a few different ways. The hollow tube can be internally threaded with an o-ring seal further in on the piston plug, but this makes wall thickness a bit greater. Likewise it can be threaded from the outside, but that makes the wall thickness that much greater. Another stunt can be a threaded extension at the end of the piston, but that increases the overall length. Finally, the sear hook can be positionable either on the piston, or in the receiver.
These adjustable features would be required on the prototypes, and be greater than a production gun. The production gun could still have the adjustments, but not to that extent, as the needed range would be worked out with the prototypes.
I'm also thinking that a ratcheting side lever may be the way to cock the thing. Let it take, say, three strokes to get it to cock.
Oh, and one last thing. This is not going to be as powerful, nor as light and handy as my .45 Colt Lightning copy, even with low powered "Cowboy Action Shooting" loads. It is, however, a very powerful human powered concept at this point.
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