Am I correct to assume that the username/password is getting cached?

probably

If so, is there a way I can reinitialize SOAP::Lite such that I can use my module as intended toggling authentication as intended?

sorry but that does not compute, maybe you want to specify credentials in the URI, as per http://cookbook.soaplite.com/#accessing%20service%20with%20basic%20authentication

Any suggestions would be greatly appreciated.

Start with proof of concept :) i mean problem :) code like this

You might find this tantalizing WSSE with XML::Compile::SOAP::WSS and Perl