CoV would be the way to go given that you only staying 2-3 months. A CoV is valid for 3 months only but can be issued back-to-back if need be.
And no, you do not require a security check for issue of a CoV, but you have to remain well clear of fenced off airports. There are plenty of other airports OCTA that are not.
The CoV can be worded as such that you wish to conduct training with a particular operator, etc. or just rec flying. If you were training, you would be with an instructor with an ASIC which would cover you anyway.
The CoV does not take long to issue. They have to check validity of your foreign licence with the overseas CAA from your home country; this can cause delays as some of these CAAs require a fee for doing this while others just take ages.
Another stumbling block is the ELP - English Language Proficiency assessment. CASA will not recognise just English Proficient on a licence or FROL - it has to have the proper ICAO grading (ie. either 4, 5 or 6) - 4 being the bare minimum to be operational.
One way to fix this is to wait til you get to Oz, and do an ELP with a CFI from a flying school (most CFIs have the CASA delegation). After you do the assessment, you can fax the form to CASA who can then complete the issue of your CoV. CASA have in the past and will, if you ask them, email the certificate to you with a a covering letter authorising you to fly off a copy of the CoV (Reg 139 I believe).
YPJT, not all clerks in CASA are inexperienced, or lack that knowledge or expertise than you think.
Hope that helps you JT.