6' by 20'??? AND your fence is already 6' high?? I'd definately recommend DEER NETTING. It's super cheap at less than $15 for a roll that is 7' by 100'. That's cheaper than any type of wire or tarp.
I used it over my run and it keeps the chickens in no problem. It wouldn't keep out a really determined predator, but it is enough to keep the chickens in, and they won't get tangled in it either. I had to use PVC pipes to make arcs across the span of the run since mine was 20 x 80 ft, and I wanted to be able to walk around in there. It is also relatively attractive - you can't really see it until you get right up on it as it is made of a very thin black nylon monofilament.
BUT if your run is really 6x20 and already 6' tall, then all you need is ONE roll and a pack of cable ties and you are set. Worst case, you would have to connect two lengths of netting together. I did that in my run since it was wider than 7' and used the cable ties for that too. Got the cable ties at the $1 store - 40 in a pack for $1. So, for less than $20 you'd have your run covered and your headache gone.
You can buy the netting at Lowes or home improvement type stores. They keep it in the area where they keep the landscape & weedblock fabric, not with the traditional fencing materials.
I'm sure you could get it online too.
Here's a pic of what it looks like:
And a pic of what my run looks like covered: