This may sound funny, but maybe it is working the way it is supposed to - pump run time, that is. Did the pump always come on immediately and shut off quickly ever since you obtained the MH? How long have you had the MH? The water heater is supposed to have some trapped air and that air can serve as an expansion chamber normally, especially if there is no check valve in the cold water feed line. It may be that the real problem was you had lost that trapped air when the pump ran the way you thought it should. Then after winterizing (draining then refilling the WH) the proper amount of air was replenished and the expansion chamber effect restored. This could be simulated by opening the WH relief valve while on water pressure (city or pump) until all the air is replaced (make sure the WH is off and water NOT hot). Then see how the water pump acts. I suspect it would act quickly, like it used to. However, in this state, the relief valve is likely to drip when the water is heated as there would be no place else for expansion. To restore the air chamber, shut off the water pressure and drain the WH, then reinstall the drain plug and apply water pressure. This little exercise might show you (we) have been chasing your tail as far as the run time of the pump is concerned.
As for the pump noise seeming to have increased...well, pumps are noisy and if it runs longer than you are accustomed then the noise may become more irritating. Just saying... Or, something has changed in the pump mounts or attached tubing to cause more noise.
