You already done this? If so, let us know what you did and how it went.
Just me, I would avoid 610 and 290 on a week day. I would rather pay the tolls on Beltway 8.
The 124 to Winnie, then 10 would be better. I would take 63 north to Liberty to avoid Mt. Belvieu traffic and Dayton red lights though. Then north on 146.