After some research it appears that Oracle/Sun may be the culprit. The certificate for JavaFX expired on 1/29/2013, so instead of fixing the certificate issue, they may have yanked it from the site entirely. Downloading and running the JavaFX SDK/Runtime doesn't appear to fix the issue yet either. It too has the same problem of the expired certificate.
WebStart seems to be the core of the problem on using the local runtime. It requires the jars that are used to be signed, even if they are local. Since the jar is signed and the certificate is expired, it is deemed untrusted.
There may be a solution by making a batch file to launch LoadUI from a batch file using the java command line?
