Is there any way I can proceed here?
Sure. Digitally sign the code with a certificate that links back to a trusted key chain.
Are only signed jar files allowed?
It is progressing towards that, yes.
Is there anyway I can tweak some settings to get unsigned applets to load?
On your own machine? Probably for a little while longer, as Oracle continues to tighten the security along the lines you have discovered.
For the users? No, nothing that is practical beyond 'educate your users as to the advantages of the digitally signed code', and to 'click OK when prompted'.