This is exactly why the technical interview process is what it is. No point wasting time asking about backgrounds and describing past projects (all of it can be easily faked). Make them write code in front of you live as part of the screening round.
I don't like making people write code live. Some really good coders just don't work well with people looking over their shoulder. I prefer giving people a take-home with an original problem to solve. Then, follow that up with a live call where you ask them some questions about it.
If they are busy interviewing, putting aside 2-3 hours (which is not much really) per interview, limits how many they are willing to do per week. As its still a candidate driven market.
Keep in mind, people have to find the spare time while doing their jobs and living life. If they have a family - good luck finding spare time :-)
The best win/win I've found is to pair with someone for about 30 minutes. You help each other, just like you do in real life.