What I think you are saying is don't publish the result until the I find a secret that matches all the results prior to that roll? Once I find a secret that matches every desired result of every roll, then I publish the roll.

Exactly!

The computational power required depends on how many rolls you want to fake. For the first one in a day it would be very easy. I think 3-4 should be possible without too much effort.

IMO publishing a hash of the secret at the start of the day would help a lot. I'm not going to say that it would be secure, but I don't currently see how you could cheat then.