I have a customer who lives off-grid out in Ojai. They run a genny about three hours every day and they have a HS Grandee. We ran a separate set of wires to the spa and connected the circ pump to that - they run it off of a battery and inverter 24-7. The tub is always hot, and always has the circ pump and ozone, but none of the other systems power up until the generator is fired up. If they use the spa outside of generator operation they do not have jets or lights, and the water temp sinks. Not as much as your would think, because there are no jets available, and they only do so in warm weather. As soon as the genny comes on line the tub reheats by itself, of course.
I think you should be able to adapt something like that: run a set of wires to your tub and run just the circ pump. You could put a 15A Edison receptacle under the hood, and a matching set of cord ends could be grafted into the pump power cord, then when you need it, you could simply swap the power over to your emergency system and run the circ pump completely apart from the spa system. That swap could be accomplished at the spa by plugging and unplugging the circ pump, or by the generator switch if you wire it all the way to the source so your don't have to dig out the access door in a storm.
Or - wire the spa with 110v from your genny switch to input numbers 5 and 6 (and ground) and the whole control system would come to life, but the (220) pumps and heater would remain offline - you get lights, temp control, settings, and circ pump only, and you can't overtax the generator because the other 'hot' wire would simply be dead, so even if you push buttons calling for jets, and the system calls for heat, nothing can happen. I would be concerned with how this type of connection would switch back and forth from the genny to regular power, but I bet you could figure it out with the right type of control switch for the generator system in your house.
Simplest: buy a submersible pump with a long power cord. Put a short piece of garden hose on the thing, and drop it into the tub - put the end of the hose into the standpipe for the 24-hour filter and you will have flow through all the systems of the spa as long as you need it, and the pump will heat the spa for you, in fact I would plug it into a table-top timer to run it only a few hours at a time so the tub doesn't overheat.
Oh - and I think Sundance uses a 220v circ pump, HS a 110v. Just sayin' ...