Not sure about battery disconnect mate, may cause you more probs than you've got at the moment. Personnally I'd say get rid of the factory immobiliser, presumably the Clifford has one included.
I've had more than 1 immobiliser & alarm system on a previous car (a hangover from previous owner having a couple of systems and me then getting a better one on but asking for the previous to still be left on there) and I had a major electrical problem related to 1 of the immobilisers kicking in but the auto electricians had a nightmare finding which one and then fault finding. I never ended up getting it fully sorted and whenever I wanted to start the car I had to lift the bonnet, put a clip on the battery pos terminal then start. I also had to stall the car each time I wanted to stop cos the only other way was to remove the clip - a total pain in the arse.
What I've come to realise is that if someone wants your car and they're a professional it really isn't going to make any difference if you've got 1 immobiliser or 100 cos they're gonna have the equipment to get past it.
If its a chancer then they're unlikely to have the knowledge to get past a decent Thatcham Cat 1 system.