Sounds like the right thing for you to do is cancel your Platinum card and use the money to purchase a United lounge membership. Amex isn't a lounge company, it's a charge card company. If I really wanted guaranteed lounge access, I'd just buy the United membership.
I look at the Amex lounges as a nicety and not a God-given right, and I'm paying $5000 a year in annual fees for two personal cards.
If I can get over it, you can too.