Any chance your D will be a National Merit Finalist?
Regarding applying to Rice, they are one of the few ‘highly rejective’ schools that give merit. But, per the 2021/22 CDS, only 32 first years received an average of $18.7K, so $35K merit is unlikely to happen…so I would NOT apply ED.
None of the Ivies offer merit aid, so unless you are OK choosing an IVY at full pay vs UTD room and board only, don’t let your D apply.
It doesn’t make sense to pay $700K-$1M dollars out of your pocket for undergrad and med school at your (recent) salary level…I encourage you to prioritize your retirement funding over your D’s college and/or med school costs.