I understand your frustration, losing links can be a major frustration and make your day horrific. There may be a solution to your problem. This add-on says it can import all the speeddial info! I found the link in the reviews for speeddial.

https://addons.mozilla.org/en-US/firefox/addon/groupspeeddial/

If you are having problems with the loss of your saved info in any other legacy extensions it is a good idea to go to the reviews of those extensions, people have been posting work arounds, possible replacements, and ways of saving lost information since the 57 upgrade.

Thanks goodwitch but this add on doesn't work

The author is very quick to reply to people having problems with his add-on. I'd suggest writing a review and asking for help.

Sorry to hear about the disruption. People use the term "speed dial" to refer to different features and extensions. Can you get more detailed about what you were using before? In particular:

Was it a speed dial add-on, or was it Firefox's built-in new tab page?

To check your disabled Legacy extensions, either:

• Ctrl+Shift+a (Mac: Command+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons
• type or paste about:addons in the address bar and press Enter/Return

In the left column of the Add-ons page, click Extensions. Then look for a link at the top of the page to Show legacy extensions. Can you identify the one were you using from that list?

If the problem is the design change for the new tab page, you can switch back to the old design:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful or accepting the risk.

(2) In the search box above the list, type or paste newt and pause while the list is filtered

(3) Double-click the browser.newtabpage.activity-stream.enabled preference to switch the value from true to false

In case we are not able to get your speed dial back up and running, please see this article: Install an older version of Firefox.