A facet pump is not designed to pump oil, its designed to pump fuel. If you want to pump oil, you need to find an oil pump. There are a number of electric dry sump racing application oil pumps out there that would work just fine for running tranny fluid through a cooler. Just have to do some searching to find them, but a fuel pump wont hold up for long in that service, either thatr or rig a secondary steering pump as your fluid pump. If you try to pump high viscosity fluids with pumps designed for low viscosity fluids, you are going to have a failure.
As far as towing is concerned, you might want to consider just going to a heavier ATF. I run the Amsoil CTL sae 50 wt synthetic ATF in mine and i tow HEAVY on a regular basis in MUCH hotter climate than you are in, or you you dont want to go quite that heavy for some odd reason the 30 wt CTJ is some pretty great stuff too ( I was running that in both my boxes, but I was getting rollover noise from my brownie so I went to the 50 in both , so I wouldnt have to keep 2 different types handy and after running it past the tech engineers at Amsoil to make sure it was a correct match, and no more noise, shifts like a dream) It all falls within allowable viscosity specs for the zf box
As far as towing is concerned, you might want to consider just going to a heavier ATF. I run the Amsoil CTL sae 50 wt synthetic ATF in mine and i tow HEAVY on a regular basis in MUCH hotter climate than you are in, or you you dont want to go quite that heavy for some odd reason the 30 wt CTJ is some pretty great stuff too ( I was running that in both my boxes, but I was getting rollover noise from my brownie so I went to the 50 in both , so I wouldnt have to keep 2 different types handy and after running it past the tech engineers at Amsoil to make sure it was a correct match, and no more noise, shifts like a dream) It all falls within allowable viscosity specs for the zf box