Welcome to the wonderful new world of telcom! I've been in this field my entire working life (39 years) and I have never seen it this bad. It seems that everyone who is out of work thinks they can do this type of work because after all, it's just cabling! I actually work on the PBX side of the business but I still have to deal with the results of some of the crappiest work that's ever been done. I mean, some of these people aren't even aware that there is such a thing as a manual on wiring with BIX equipment (there is, i keep a copy on my PC to show it to these morons, assuming some of them can read).
In any case, to do it right, it's going to cost a bit more money and unfortunately you're going to be competing against people who will undercut you no matter what price you put on it because they will do it cheaper by cutting corners and using the cheapest material around. Be thankful though that the customer is willing to have you back to terminate and test. At least that way you can maintain some control of the end quality.
If I were in your situation, I would charge them 3 times what the box of cable cost me. If they're willing to pay it, great! In the end, it might even cost them more overall depending on how much they pay these goons. If you have a written agreement with the customer you might want to consider a disclaimer in there stating that you are only responsible for the work you do and specifically exclude anything to do with issues reulting from the running of the cable including damage to ceiling, ceiling tiles, walls etc..
Hell, I remember one site where the cusomer offered a few of their employees a case of beer to run 35 cables into their offices. These guys ran those cables everywhere, thru anything to get there, and when they got them down the walls they literally punched a hole in it with a screwdriver, pulled a couple of feet through and considered it complete. They ran them all into the comms room through a hole that was literally punched through with their fist and left them in a tangled mess on the floor and not a number or any identifying mark on any of them. I was sent there to install the phone system and they expected me to provide jacks and terminate everything. That was NOT in our contract so you can imagine what my response was. And oh ya, the cable they used was the stuff used to make patch cords with, not the the standard solid core 24 guage stuff. We brought in one of our cabling contractors and he charged them an astronomical amount to finish the job and neither of us would guaranty anything for them.
Just goes to show you. It's not just the mess of unprofessional, uneducated buffoons that have infiltrated our profession, it's also the cheap ass customers willing to go along with them and then expect the real pros to fix everything that's messed up for nothing.
Everytime I find myself in your situation, I make sure I charge enough so it turns out to be more expensive for them in the long run. If they don't call back, then who cares. I refuse to work for peanuts. I've spent a lifetime learning what I know and if some newbie thinks they can do it better than I can, they can take their best shot!
Good Luck.
