So as I stated, you'd just fill out the OG tags (optional), then get whatever code you need from the other social platforms and dynamically create the "share" buttons with the data needed. As long as you have the code needed from the social platforms, you can create your own share button. My concern with doing it this way, is you're probably still going to have to link back to those social platforms with some js or other files so you'll still have http requests and they could be a lot if you have a lot of share buttons.
Just trying to confirm, you can for certain state the site went unresponsive because of the additional http requests for the share buttons? There may be other options like optimizing webparts and cache in Kentico and the server which will also help your performance.