It's very unlikely you'll be allowed to leave Taleb Larbi border post without an escort - probably organised by the same agency that supplied the Alg visa and costing €100/day with a car + driver. Others have tried and failed here over the years.
If you want to try and slip into Algeria and not get bogged down in this way, I suggest you fly into Algiers airport while trying not to look like backpackers. I did so last month and walked right through unchallenged, although on previous occasions (possibly at a time when more bombs were going off in Algiers) immigration asked where my escort was. On all occasions I have an escort/local contact waiting for me somewhere, so am not trying get away with it.
If that works, once in the country stay north of In Salah latitude. If you want to get down deep south (Tam/Djanet), I propose a domestic flight (€100?) and then be prepared to deal with any land transport issues coming back up (or fly back to the north). Having said that, I dont think you will get away with it arriving in Djanet where they may be more strict. In Tam - flying in direct from Europe - again we have never been asked for escorts by immigration (though they were there waiting). So if you want to see both, go to Tam first, then fly to Djanet, and be prepared to face the music there. Things may be more edgy here for tourists following Italian kidnap
I take it you have read this post
and have taken on board what it says.