Is Google able to see child pages in our AJAX pagination?

[Jason.Capshaw]

We upgraded our site to a new platform the first week of August.  The product listing pages have a canonical issue.  Page 2 of the paginated series has a canonical pointing to page 1 of the series.  Google lists this as a "mistake" and we're planning on implementing best practice (https://webmasters.googleblog.com/2013/04/5-common-mistakes-with-relcanonical.html)  We want to implement rel=next,prev.

The URLs are constructed using a hashtag and a string of query parameters.  You'll notice that these parameters are  &parameter:value vs &parameter=value.

/products#facet:&productBeginIndex:0&orderBy:&pageView:grid&minPrice:&maxPrice:&pageSize:&

None of the URLs are included in any indexed URLs because the canonical is the page URL without the AJAX parameters.  So these results are expected.

• Screamingfrog only finds the product links on page 1 and doesn't move to page 2.  The link to page 2 is AJAX.  ScreamingFrog only crawls AJAX if its in Google's deprecated recommendations as far as I know.
• The "facet" parameter is noted in search console, but the example URLs are for an unrelated URL that uses the "?facet=" format.  None of the other parameters have been added by Google to the console.  Other unrelated parameters from the new site are in the console.
• When using the fetch as Google tool, Google ignores everything after the "#" and shows only the main URL.  I tested to see if it was just pulling the canonical of the page for the test, but that was not the case.
• None of the "#facet" strings appear in the Moz crawl

I don't think Google is reading the "productBeginIndex" to specify the start of a page 2 and so on.  One thought is to add the parameter in search console, remove the canonical, and test one category to see how Google treats the pages.

Making the URLs SEO friendly (/page2.../page3) is a heavy lift.

Any ideas how to diagnose/solve this issue?