The logic of other members isn't wrong!
See, the point of Rajdhani is to provide fastest connectivity from state capital to national capital, and usually by shortest route. There is a bit of leeway provided in second clause, but the cases don't justify increasing travel time by multiple hours as would be required in your case.
See, a Raj is created for state capital, and as such majority quota is blocked out for end to end passengers; SR bound raj don't follow this as they don't have much E-E passengers but the ones...
more... starting from Mumbai won't get that exception. With that rule, hardly any seats would be available for Rajasthan based passengers and thus would hardly provide any use; a Duronto or even better, an SFE would serve your cause better.
The Era of Rajdhani having much shorter travel time is behind us, as many trains are getting 130 kmph sanctions and seeing reduction in travel times now. The route via rajasthan isn't suitable for 130 so not much benefit would be gained by change of state anyways!