I am probably being somewhat crazy even considering this, but how doable is the below do you (FT / India experts) think? Have a narrow (very narrow) window for a trip, holidays I can't carry over and saw a nice fare I can use an expiring upgrade voucher for business class on....

Arrive DEL Wednesday morning (before 9am) - get car to Agra
Wednesday afternoon and part of Thursday in Agra - car to Jaipur on Thursday afternoon
Friday in Jaipur
Car to Delhi on Saturday morning - drop bag at airport hotel and do some sightseeing / meet friend for lunch / dinner if around, catch flight home a bit after midnight

Am wondering if it's better to stay Agra on Thursday night and only leave Jaipur on Saturday afternoon - and drag friend out to an airport hotel for dinner on Saturday night... Trying to nail down my thinking before I mention that I might be in the vicinity!

(Thanks in advance - and I am cheating somewhat as I did spend a few days in Mumbai for work years back, so first time holiday in India!)