Right, that's a solid effort for the budget. Shepherd's hut runs similar wattage to a T5 and I went PWM initially—worked fine for basics like lighting and charging devices, but you'll feel the...
Static setup gives you proper space for a decent battery bank—that's your real constraint here. Before jumping to a 3kW unit, sort your batteries first. What capacity you running currently?
Mate, it's doable but @MoorKev's not wrong about the draw. Single-ring induction pulls about 2-3kW, which is brutal on batteries.
I've got a similar setup in my hut and ran the numbers before...
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