This will be quite a challenge.
Picking a power wheelchair with rehab seating (leg lift, recline, tilt, elevate) is hard enough without constraining the weight of the wheelchair. I can't imagine doing so with the kind of weight limit you referred to.
I have had 7 wheelchairs, 6 of which have been Permobil. All those Permobil wheelchairs have weighed over 400 pounds.
My only wheelchair that weighs less than 400 pounds is one without rehab seating.
But, even if the wheelchair is less than 400 pounds, how much equipment will it need to carry. I carry a backpack with various supplies and often have my Resmed Astral 150 bipap (ventilator) on the back. I use special seat cushions, lateral thoracic supports, lateral thigh supports, and headrest, which can add additional weight.
Besides the weight limit, you should also carefully investigate the dimensions of the elevator. I have been in two houses with residential style elevators. My wheelchair barely fit (physically) in one and did not fit in the other. I did not think to inquire about weight restrictions in either situation.
Of course I don't know what drove the decision to get an elevator with a 580 pound capacity, but to me the best solution would be to pick a different elevator with a higher capacity. I am guessing that is easier said than done.
With that said, there are ways to reduce the weight of a wheelchair. Many wheelchairs use a pair of group 24 lead acid batteries. These are large and heavy. Quite a few of those wheelchairs will allow a lighter pair of group 36 batteries instead of the group 24 batteries. Of course, the wheelchair will have a substantially shorter range if that is done. That range reduction would be unacceptable to me.
It is also possible to replace the heavy lead acid batteries with substantially lighter lithium batteries (specifically, Lithium Ferrous Phosphate). These will be lighter, but require advanced skills to assemble and maintain. I have put lithiums in one of my wheelchairs. It was a fun project, but was fraught with adventure, risk, and cost. I don't recommend this for the typical wheelchair user. I don't know of any practical off-the-shelf options for lithium batteries for the type power wheelchairs your PALS will need.
What I would not do is to overload the elevator. In fact, I would want to stay well below the limit allowed by the manufacturer.
Steve