By purchasing a burner phone, I am definitely traceable by law enforcement. You want to be untraceable after a crime - I'm not solving that problem.
Your other suggestions are fine ideas, there's not a specific right or wrong way to do it.
Well, it really depends on how you buy it and where you use it. Yes, they can locate your phone based on triangulation. However, you can buy a prepaid burner phone outside of your area and then use it to create a Google account and then make sure you are using a VPN when connecting from a residential location. However, I don't really see the use in buying a burner phone just to download APKs from. You can do the same without one. I agree, that it does work to accomplish what you mentioned but I was just trying to explain that there is a much easier route without the additional burden.
You seem to have missed the biggest part of why I recommend this to some people - never, ever put a SIM in the burner phone. It's just for that burner gmail address you use to get into the Google Walled Garden.
It looks like there's no proof either way. Are you testing without a SIM card?