This is manageable with the right kayak system (IMO). I run Red-5 up the PK/Brazos river at 500-600 late last year. My Hobie pedal system allowed me to push my kayak towards the dam. Although, a little more strength and repetition with my foot pedaling, I was able to get to the dam at about 40 minutes. Now, using your arm strength for paddling, may/will be a bit of a struggle. I'd recommend going only a short distance past the bridge. Stay closer to launch point in case of unforeseen circumstances. Stay Safe!
Bruce V....Seriously, The real Bruce Lee;-)