Take a look at where the new saddle makes contact with your body an try to match the fit of the old one. I had those symptoms but was cured by adjusting fit. In my case it was a combination of cleats too far forward, saddle too high, and saddle too far rearward.
The change resulted in a fit where the saddle did not contact the inflamed bursa over the course of the pedal stroke, but applied pressure properly on the sit bones instead.
Use of a bike trainer at 15-30 minute stints per fit trial were helpful.
Best of luck.