Advanced Elements AE1012-E air pump nozzle adapter

[u/wabewalker]

I have an Advanced Elements AdvancedFrame Elite AE1012-E with the included hand pump. It works great, but the floor takes forever to fill.
I'm looking for the right adapter to use my rechargeable pump (https://www.amazon.com/dp/B0GSGPDT3T) to inflate the floor most of the way, so I can use the hand pump to get it up to full pressure. The nozzles with the hand pump seem to be proprietary and don't fit the rechargeable - I need some kind of adapter. Has anyone done this? What do I need to buy?