It has a pump. If the fluid isn't thin enough, it won't flow easily.
As a 1st choice, stick with ANY full synthetic ATF.
Ams MTF and RL MTL are a tad thicker and should shear a point of so. Being a full synthetic(and thin compared to gear oil), should prevent any fluid pumping issues. I would not go any thicker then that. Is thicker even needed when average temp in your location isn't too hot?
RP also has a MTF that is the correct visc.
ATF+4 embarassed Mercon/DexronIII/ATF+2 when measuring chain stretch, general tranny wear(gears bearings...)in Chrysler transmissions. It would be an economical upgrade that exceeds Dex/Mer/cheap ATFs.
Regardless of fluid, those 10k intervals should be considered.