My advice, and what has worked for me:

Hills are about having a plan, and executing the plan. Decide whether you are going to spin the hill or mash the hill before it starts. Are you going to build speed before to carry you over, or be steady throughout? Decide before the hill decides for you.

Rear shifting works fine under load, front not so much. Decide which ring you want to be in before you are in the death mash. If the hill is going to require your small front ring, be on it early, even if it means you are on smaller cogs in the back. It is easier on the system to bail out just on the cassette. The only times I have ever thrown the chain is when bad planning forced a front shift under high load.

Stand up with a purpose. If you are alternating randomly between standing and sitting you may be wasting more than you gain. Stand to pick up speed, and raise your cadence to a spot where you can get sitting and spinning again. Stand to finish a hill, and crest strong.

My final thought: hills should hurt. Spinning up a hill is a misnomer. If you maintain 90 cadence over a hill, you probably have geared down so low that you are crawling. I know many folks who spin up every hill, and usually the key to success is a mixture of mash and spin.