You have the command thrust lower unit, so it carries the larger V6 prop selections. It already pushes a lot of water with the larger diameter props. I hope you get it sorted.
Does it need stern lift, or just some pop to get out of the hole? I think the max rpm for the CT version is slightly less than the standard leg. Make sure you're using that spec as you try to prop for max rpm's. (edit...rpm range identical for both versions)
Mercury says: Command Thrust (CT) models have a gearcase with a larger torpedo and a bigger-diameter prop. CT can lift a heavy boat onto plane more easily and hold it there at lower speeds without impacting top speed.
Available Command Thrust gearcase for 40 / 50 / 60hp Four Stroke models offers more control, improved hole shot and enhanced mid-range power. The combination of a gearcase that sits deeper in the water, a bigger prop with 20 percent more blade surface, and lower gear ratio provide unmatched thrust, maneuverability and boat lift.
Your CT 60 weighs 260, the 90 and 90 CT weigh 359 and 363 respectively.