Velox rim tape is great. I don't use tire liners. I will make a boot if I have a cut or puncture in the tire and don't think it needs total replacement.
Having a problem with double flats suggests to me that you're either running over a lot of stuff you shouldn't be running over (glass, etc.) or you aren't inflating your tires to the correct pressure. Hit one good hole with too low pressure and you're asking for a double pinch flat.
I use "race" tires all year and generally don't have problems. When dealing with road salt, gravel, etc. I will more frequently inspect for cuts and debris stuck in the tire.
Another common cause for chronic flats is having a valve stem hole that is sharp. This would tend to promote ripping at the valve stem attachment to the tube. It's not easily fixed with rim tape like sharp spoke holes, for obvious reasons.
Wow! Great conversation! Thanks for the proper definitions- I do have cloth rim strips- had plastic previously and that was definately the cause of multiple flats on my rear tire so that problem should be fixed. And now that too low tire pressure has been brought up, I believe that may have been a cause of my double flat situation. And I do realize that sometimes it is just bad luck- I also ran over a huge carpenter's staple once- but this frequency was more than just that. Thanks for all the help!