That is close to what needs done before you change pads. Too often people just push them in which pushes in the old build up. Then the calipers don't work smoothly and brakes wear poorly or not work well at all. Again I hesitate to mention the best way is to replace the seals lol. I have actually taken them all the way apart, put the old seals into clean fluid while I degunked the bores and recesses for the seals. Then use a finger nail to clean the seals and reassemble. Most of the time that works just fine even if the outer dust seals have some tears or wear. Here's the right way:
I agree with Sean, I would always disassemble the calipers, removing the pistons, to expose the creeping crud trying to bollox the proper operation. Consider what's at stake here! Merely your brakes' operation and that which depends upon your brakes-your life.
You had success in the stop-gap method of servicing, now, do it properly!
In the pics below I use a grease gun to deliver > 5X the force that even a 175 psi air compressor can deliver to dislodge the stuck pistons in a frozen brake caliper. I've never been defeated by a caliper using this method. You do need to thoroughly-clean all the grease out, but you should be doing a complete cleaning anyway once the pistons are out, so it's really no extra work.
Pic #4 shows a tool I use to drive-out a stuck master cyl piston, though it's only of-use if your hydraulic hose female in the master cyl is inline with the piston shaft. It doesn't work with the VMax 90 degree point of hose attachment.