I am not sure if this is the best place to ask this question. Moderators are welcome to move the thread to an appropriate forum.

I am trying to book a hotel room in Taj Lake Palace, Udaipur, India for my parents using the points from either American Express, Delta or AA.
Of course, I would like to book using the minimum number of points.

I have 25000 points in Amex, 10000 points in SPG, 70000 points in Delta, 60000 points in AA and about 20000 Thankyou points.
We have some other accounts at Delta, Amex, AA and Thankyou where we have some more points ranging between 10K -25K.

Now if I book by cash it will cost me around $380 including taxes.
1. In american express I can see booking in two ways:
one would be via travel and then pay with points - that seems to cost around 80K points
other way is to use "Leading Hotels" certificate which costs 70K points.
2. Delta seems to be cheapest it costs 53K Delta miles.
3. AA site is quite strange. Now if I try hotels link on aa.com, it directs me to AAVacations site and it offers me the price of $380 but if I use the link in redeem miles section, it still directs me to AAVacations but this time shows me price of $533 and costs 80K AA miles.

So, is there any other (cheaper) way to book this hotel room?
Thanks in advance for suggestions.

ps. If it matters I need to book the room for one night from June 27 to June 28.