After heavy use, my big iPad has charged very slowly. What can I do besides the Genius Bar? Is there a different wall charger I should use? During an inpatient stay, I had my 12.9” iPad Pro(Model A1652 EMC 2827), which I tried to use much of the time I was awake. The battery was depleted most of the time: I had it plugged into a wall charger, and power was never really more than 5-10%. It lost power frequently. I took it to the Apple Store and was offered immediate replacement. 

Now my laptop is in the shop, so I have been working from my iPad, and its apparent charging behavior is similar or worse. Besides that the charge has usually gotten down to 10% and stayed there during the day, an overnight charge while powered off from a wall socket only gets it to around 25%. I get the impression, possibly a false impression, that you ride it too hard and it becomes permanently sapped. 

I have read in other posts that iPads need more current than an iPhone, so possibly a different charger would help. Beyond that, what can I do beyond replacing it with an un-sapped model so it will charge from either U.S. or continental Europe power?

Thanks,
iPads do need more current than iPhones, they have bigger batteries, and bigger screens. They consume more power because of this. If you aren't using a charger (block) of the same or higher capacity than the one included with your iPad. Considering this is a Pro model we're talking about, it'll probably have to be a higher voltage charger than a regular iPad charging brick. If you ARE using the charger included with your iPad Pro, consider getting it replaced. It may have given out from a power surge, or just worn out from constant use.

Temporarily, however, you can power off your iPad while charging. I've had a similar problem to this with my Samsung Tab A 7.0, and powering it off allows it to charge. It will probably still charge slow, but it won't lose battery life, and will charge significantly faster than with it powered on.