You are platinum with Hyatt. For that you think some hotel will comp you elite?? Good luck, you really have little loyality "value" to trade.
The suggestions to contact the hotel you will be staying out for "lets make a deal" is still a good one. IF you will be generating a lot of nights at one hotel, especially if they are running on the low side of the occupancy curve, then you stand a chance. Find out who is the General Mangager and pitch him/her, in person (on first stay) or my mail. You will not likely get a "status leveL" but you might be able to be treated as such when you stay there without the additional payment.
As to the discouragement in the first paragraph, do not let that keep you from trying, if you can stand the time and disappointment, good stuff sometimes does happen!!