For the two 30' low-yield shallow wells that I've been dealing with, both have FloTec 1/2HP 4" submersible well pumps. These are nominally rated at 10 GPM. They are both 230V, but their comparable 115V model is otherwise identical in specifications. I see no reason why the FloTec pump you first tried would not have worked; the second 1 HP pump is overkill for such a shallow well.
OP, when you first start the pump, do you see a burst of high-flow water out the discharge followed by the 1 GPM low-flow? Or is it always just a 1 GPM flow, even when the pump first starts? From what you've described so far, it doesn't sound like your pump is draining your well of water. I would think if that were happening, then you'd first see 5+ gallons pump out at a very high flow rate, followed by a lot of gurgling, spurting, and intermittent flow at the discharge as the pump sucks air. But one way to be sure would be to run a garden hose into your well as the pump is running. If your hose is flowing more into the well than what's coming out the pump's discharge, then you know you're not overdrawing the well.
From your description of the symptoms, my guess is that your problem is one of pump intake obstruction. A 4" diameter Sch40 PVC well casing is 3.99 - 4.03" in internal diameter. The FloTec pump, for example, is 3.78" in outside diameter. The pump's intake is at the midpoint of its body, which means water below the pump must squeeze past the motor housing to get to the intake, while water above the pump must squeeze past the impeller housing to get to the intake. Subtracting the cross-sectional area of the pump body from the internal cross-sectional area of the well casing leaves you with only 1.34 square inches of space for the water to flow. That is the equivalent of a 1-1/4" Sch 40 PVC pipe, so it should be fine. But what if there are mineral deposits or some other build-up encrusting the inside of the well casing? I don't know how likely that is for your well, but I've read that when a well is repeatedly pumped dry (as is common for shallow, low-yield wells), that mineral scale and slime bacteria can build-up on the casing, particularly on the screen or the part of the pipe that is slotted. You mentioned that the old pump was rusty and clogged. What was clogging that old pump?