The best technique is to do as much spraying as possible in the plane of the bike, rather than from the side. So blast down from above, up from below (except not at the headset) and from the front and back. I understand that sometimes cleanliness requires some blasting from the side, and if it is just at the frame, no harm done. But blasting into jockey wheels, bottom brackets, pedals, and hub bearings is a bad idea.
Addressing your creaks associated with power washing, the first thing you should always do after washing a bike, whether with a power washer or a hose or bucket, is remove the seatpost and turn the bike upside down to let the water drain out of the seat tube. Do this after every ride in the rain as well.
Often the creaking is the leather at the edge of the saddle shell rubbing on the saddle rail clamp when your weight brings the two into contact. When the leather dries out, this rubbing will result in creaking, so applying grease to the edge of the saddle shell there can fix your problem.
Obviously, after power washing, lube your chain every time (actually, do it after every ride) and jockey wheels after every few times. The chain is a place for the spray lube you mention; on other parts it will have a transient benefit at best. With cartridge-bearing jockey wheels, pry the dust cover off of the bearing with a razor blade and squeeze some grease in there before replacing the dust cover.
Creaking in the crank and bottom bracket area is often coming from around the bearings. With a threaded bottom bracket, unscrewing the cups, greasing the threads, and tightening them back in to full torque spec will often fix it; plumber’s tape on the threads of a persistent creaker might help too. Also with a press-in bottom bracket, you may need to remove the cartridge bearings, put grease around them, and push them back in