I just realized that it's the Texas Eagle that (I believe) gets joined to the Sunset Limited, not the Heartland Flyer (not sure how I got confused there). I have no clue what the Flyer's on-time record is, so I don't know what the chances of making or missing that connection are. Since it's a shorter corridor, though, I wouldn't be surprised if it runs pretty much on time.

Also, Amtrak operates a Thruway coach from Tulsa to Oklahoma City that has a guaranteed connection with the Heartland Flyer (Amtrak Thruway buses are usually much nicer than their Greyhound counterparts), so if you want to look into Amtrak, that would reduce the driving time for you a bit. The bus actually runs from Kansas City to Oklahoma City, but the only other stop is Bartlesville, which isn't really any closer than Tulsa.