Love it!!! VERY well done!! Since we've redone both our bathroom I was having issues with my suction cups, too, unless I used the glass shower door, but that is proving to be somewhat of a PITA, so I may have to copy your great idea.
Super easy just two five foot pipes two T's and six 90* elbows. And of course the ever present vet wrap for grip. Took me less than a 1/2 hour to make.
I have that same corner rack in my shower. I just park Parker on the bottom shelf and point the spray to one side of the caddy (so he can get away from direct spray if he wants to). He will go into the direct spray on his own for a minute, then he's done.
I had a lady in one of my dog training classes a few years ago that had a Grey she'd take in the shower with her. Yeah, she suffered an unfortunate "nip."