They've really ramped up selling Prime in the checkout process. It's no longer easy to order from Amazon; it's this adversarial "spot the 5 traps" obstacle course where you have to avoid clicking the "sign me up for Prime" trick buttons.
I've noticed this as well. The trick is to _remove your credit card_ from your Amazon account. It significantly reduces the "traps" and prevents them from automatically subscribing you to Prime. I now purchase Amazon Gift cards instead (also, free shipping when using a gift card).
Oh hmm, the gift cards thing -- are the gift cards no-overhead? Like, can you buy a $100 gift card for yourself for $100, and then use it to buy things with free shipping?
Yes, exactly! In Japan there's also no fees or sales tax on Amazon gift cards (physical ones), and you can purchase them in arbitrary amounts I think max 100,000 JPY (~$1000 USD). Amazon.com provides one-day free shipping with gift card purchases, but could have a surcharge for oversized, heavy, or international items. I'm not sure if any of this applies to digital gift cards though.