I'd be inclined to stay on US 290 to Brenham, follow TX 36 to Milano and join US 190 there at Milano. (US 290 is a TOTSO in Brenham, so one just stays on the highway which continues as TX 36.)
Not sure the current state of road construction of I-35 in Temple, but it is still likely to be faster than tracking southward into Austin (ie US 290 to US 183), not to mention seeing the I-14 signage along US 190 thru Belton-Killeen.
If you have the time, you'll be going very close to the Regency Bridge, near Goldthwaite.
Been too long since I've veered further west to comment further.
Have a great trip.