Years ago I was flown out to Amazon to interview for them. I had like five interviews that day, all from different teams who were all asking questions that had nothing to do with the job I was applying for, never asking about my relevant experience. They were asking me CS questions and I had never gone to college. They asked about computer design - like, draw a diagram of a computer (I had never made a diagram before) and explain how the northbridge on the motherboard works (this was a while ago). Granted, I could have taught myself a lot of that, and I had a general idea about most of it, but they also just could have said "We are looking for someone who has the same skills and knowledge of a Computer Science graduate", and I probably wouldn't have gotten on the plane.
So perhaps a big part of the problem is figuring out what candidates you want to interview first. A lot of these questions are designed just to rule out people who aren't very logical or won't take the time to do it properly, and I understand that.
A manager once told me about a hire they had to fire on the first day. They did a lot of interviews remotely as he was in India. When they finally flew the guy in and put him in the chair, he was a different person. Literally. He had someone else do all the interviews for him so he could get in the door. Pretty weird that he thought they wouldn't notice, but people are that weird sometimes.
If you have too many hires to do, it sounds like you either need to outsource hiring, or build an internal hiring team that can do the technical interviews. This could be a semi-global or traveling team if you're often looking at non-local talent. Or they could do a lot of interviewing via webcam, perhaps with a second webcam shipped by Amazon (it's not like you don't have cheap shipping already) the user could point at their own screen for extra security.