Hey John. I don't have an answer for you but wanted to let you know that SourceCoast has been burning the midnight oil on a couple of updates and a big Joomla trade-show. They have been very quick to respond/resolve in the past so hang in there a bit longer.
As for the iFrame with our PHP method, you may be able to do that. Never tried it though, so it depends on how much you want to dig. Mainly, when the Login With LinkedIn button is clicked, we call the "linkedInAuthenticate" function from the /components/com_jlinked/controller.php file. That code is only about 5 lines long, and the last 2 are performing the redirect. You could try using the first 3 lines to get the URL to redirect to and then showing that URL in an iFrame. That should work, but I'm not sure how the redirect will work when the user completes the login.
If that's over your head, just let me know and I can help you understand the iFrame a bit better.. I think you probably can take it from here though (gauging from previous conversations).
It's something we plan to look into, but if you're already doing some of the lifting, we'll gladly go for it now!