Yeah the spec calls for a new outline in each section, so multiple H1's are technically allowed, but assistive technologies and (as much as I hate this argument) SEO don't always line up with the spec. So for now it's safer to go the 1 H1 route.
Usually I use W3C's validator (validator.w3.org/nu) with the outline option checked to test for at least the basics.
Then there's some other tools (like the "Siteimprove Accessibility Checker" plugin for Chrome) that help a bunch as well (but they focus less on semantics and more on pure a11y).
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