After I got all the warp wound on to the warp beam and started weaving, I was completely frustrated with how uneven the tension was. I needed a better solution.
I rotated my loom to face the banister. I unwound the whole warp and cut off the 4 inches that I had already woven. I hung the warp over the banister and tied sections of it to water bottles to get even tension across all the warp.
I rewound the entire warp and ended up with a very even tension for the rest of the project. Success!