All fuses are rated according to their impulse capability in terms of I^2t because their cold resistance varies with rating. But the true power calcul ation is I*2Rt.
Every protection device must have a time constant faster than the failure m ode it is protecting, which implies a smaller mass or accelerated by magnet ic or thermal forces.
I can remember blowing breakers due to induction motors starting up and wis h I had a better means to control the starting current at the expense of st arting torque or no-load waiting time while getting up to speed.
Other than a variable speed controller, a simple solution is s thermal brea ker which ought to be embedded in the motor assembly. In the early days a fan fail circuit that might overheat with s stuck rotor consisted of a heat er resistor and bi-metallic strip bonded together in line with air flow. N ow you can use a PTC which regulates to 85'C upon short circuit and thus re sistance and power depends on max sustained current for required voltage an d size.
In this case I suspect, you have two reasons;
1) to avoid false tripping due to over-sensitive slow-blow fuses
2) provide safety by reaching 85'C faster than any bad contact. This is ha rd to predict if your wiring has or will have any bad connections.
There are standards for thermal breakers for I^2t time constants and is you r best bet, albeit may be a little expensive for 2phase breaker.
Another alternative are PTC's which may be ganged in parallel if thermally coupled but exposed to air for rapid resettable air fuse characteristics. They regulate to 85'C on short circuit but run cool in normal operation due to several decade range in variable resistance.
You might consider two (2x) 4 Amp PTC's in parallel, where 4 Amp is the tri p current which is 2x the Hold current and trips in < 30 sec @ 5x hold curr ent rating. Verify specs if this works for you. Cost $2.84 each. 0.5" pitch radial capacitor-like thin body using metal oxide material in epoxy... I think this is what they use in DC motors for cars such as for power windows . Include voltage margin to rating.
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