We've been going to the Med Center often here lately. Since the 288 toll road construction seems complete, the traffic has gotten much better. We usually hit it anywhere from 6am to 8am and again mid day going home. In the past I have even gotten off the freeway and driven through downtown.
I would just go for it. You have just as much a chance of getting in a jam on 59/69 inbound. You only have to move over 1 lane to the left around George Brown Convention Center then take the 288 exit.
But I've driven in Houston traffic since I got my license...1965.