Just don't underestimate how hot it will be. Oklahoma and Texas are pretty scorching by May and June, so I would personally go with April-May.

Most of my family lives in/around Tulsa, OK and I may be moving there soon. I personally would love to take a tour around OK. Beautiful stuff.

Looking at your route, it looks like you are staying away from the 'large' cities, so you shouldn't have to worry to much about being killed in traffic =P. Those lake stops should be very nice as well. One thing I would take a look at though is how well you should pack. I haven't been out to that part of OK or TX in a long time so I don't really remember how far of a distance you would have in between decent places to resupply and grab food, but I don't think it is so bad.

Those lakes look nice as well =D