Yorai,
You're correct, it's not a fun issue to experience and there's only limited things that we can do within JFBConnect. The Force Scheme option is one of them. By enabling that, all Like buttons and Comment areas will use http, which means your old counts should still work. It also means that any new pages on your site will be shared with http, which may or may not be ok. In general, your site likely redirects all requests from http to https, which means that Facebook will follow these links as well. The count will be for the http page, but the users will be redirected properly to the https page.
It's not ideal, but it usually works.
One other option, depending on the amount of pages that you're using the sharing features on, is to include the share buttons manually on those older pages (or at least the critical ones that had a bigger following) using the old link. Then, you can use our automated tools to add the share buttons to new pages and exclude automatically adding those buttons to the old pages. It's a bit tedious, and in years you'd still need to ensure the old links are correct, which is a pain.
That's about it for options. Even in the first link that you mention about 'recovering' those links, there's a disclaimer at the bottom of:
Please note: Due to recent (early 2017) changes to many social network APIs, Social Warfare cannot guarantee recovery of shares from networks other than Pinterest and LinkedIn.
Basically, even with the best efforts, Facebook could change their algorithm one day to not follow redirects, which would mean that your pages that still linked to the http version could lose their count someday in the future when they've amassed an even bigger count.
For that reason alone, we recommend just making the hard break to https and starting the process of garnering the count again, no matter how annoying that is.
I hope that explains further, but please don't hesitate to get in touch if you have any further questions.
Thanks,
Alex