I've never used a Zippo for pipes, just butane. I'm a Harry method guy too, and it's just as good a way to pack the pipe as any other. Sounds like you just need to get used to the pipe gizmo on your zippo or use a different primary ignition source.
Strike anywhere matches are becoming hard to find around here. The stores only want to sell safety (strike on the box) matches. So I mostly use a butane lighter.
But I still want one of these:
I use a Zippo with pipe insert and have no problems with relights. I also use Ronsonol fuel and don't have a problem with the taste. I do use Zippo flints. In my experience, the no. 1 good quality of a Zippo is reliability; my Zippo has never let me down. I have an Old Boy here that needs to be sent in for repairs because it is leaking butane badly. It's a wonderful lighter when it works but I was disappointed when it failed me because it cost as much as 4 Zippos. And Zippos are still made in America.
Smokey