I don't think that a new modem would help. I've been through three different modems at this point, and it's not like the current modem is incapable of reaching 35 Mbps upload... it's just not available to me most of the time, like you describe. I've been having issues with my upload for several months now, but it's been almost unusable for the past 6 weeks. I've had days where I can't even do voice calls with friends and family because the upload drops so low. Customer service upgraded me to a gigablast package as a trial because this was affecting my business, and unfortunately my upload speeds were literally no different, sitting around 0-5 Mbps most of the day. I can no longer reach an American call center to get me off the upgraded plan (which was meant to be a trial) or reimburse me.
I had serious issues with my upload once before, and the problem that time ended up being damaged lines at a few other homes in the area. Whenever those people used the internet, it would create upstream noise and mess up everyone else's connection. My upload was perfect for several months after the lines were fixed, but this time I've been through literally a dozen tech visits with no change. I would honestly suggest trying another service provider if you can. I'm looking forward to moving next year and not dealing with Cox any more.