I was initially writing an "is this possible?" type post when about half-way through I had a look at the SemiSecure Login Reimagined plugin page and noticed the devloper had finally responded to my question - which was is it possible to integrate it with the Mingle login page? His reply (found here) contained a link to a plugin he'd written that attempts to integrate SLR with the majority of login forms currently available.
To install it just copy/paste the code on that page into a blank text file and save it as something like "Semisecure Generic Frontend Integration.php" - use whatever name you want but make sure you give it a ".php" extension, then upload it to your "plugins" directory, login to your admin area and activate it via the "Plugins" page.
Why am I writing this post? This is something I've invested the best part of a month researching so if this saves even just one person having to go through the same agony I'll be happy! :-D
Even the developer states that it's not guaranteed to work in all situations, and some scenarios - such as having a login box widget in the sidebar - may cause further issues, but it does seem to work with the Mingle login page so it should work with other similar forms.