< deleted >
You're asking a question that really can't be answered over the internet. There are too many variables. We cannot see where the six locations are, how the walls line up from the first floor to the second floor, whether or not the basement ceiling is finished or not, type of construction of the home (balloon framing, post & beam, western platform framing, etc), plus you are trying to not go into the attic, which would be the easiest way to access your second floor locations.
Other than generalized tips, such as those in the link in the previous response, you're on your own.
You say that "The phone system is utilizing the VoiP protocol. The router also carries all the data for the house, but that's not the purpose for these runs."
I'm like some of the others who have posted replies. If we knew more about what you have and what you're trying to do, it would be easier to propose some solutions that might be less difficult and cheaper than running Cat5.
1. What's the purpose for the Cat 5 runs; is it strictly for your phones?
2. How does the router carry "all the data for the house; is it a wireless router?"
3. Do you have an older home which has no phone jacks where you need them; if so, why not a wireless phone system?
Have you consider wireless? It's much simpler.
If you connect a newer wireless phone directly to the router/voip unit, then you can add additional units from the same maker wirelessly. A few maker sell these phone as a set. It'll probably run you a couple hundred bucks to get 6 units but it sure beats the fishing wire.
Nice discussion, I was wondering if I can pose another sidebar to the challenge. I am running into a similar issue on running Coax and speaker wire. The run is going from the unfinished portion of my basement, through a linen closet then up to my attic. Then fish the wire from the attic down into the first floor walls.
What I am curious is what issues might I have if I run the wires through a pvc pipe in the linen closet? Or how big of pipe should I consider from an expandability perspective?
Any insight would be appreciated.