Tyre Question

I'll ask the collective wisdom of this group. What tyres would you suggest for a 2001 78 Series Troopy. I go out at least once a month with a 4wd club in some fairly rugged country (gorges around Armidale, NSW). I'm also going to do Madigan's line (North Simpson Desert) in August. The troopy will have lockers in another few weeks.

Current tyre - Dunlop Road Grippers - and they have suprised me...not as awful as I thought, but I really do need more grip when rock crawling, or doing river runs (Mud, shingle, sand and rocks....lots of rocks)

Here are the constraints.

* I don't want to put flares on the troopy (The club has someone rip a flare off about once a trip....just that sort of country) so REALLY wide tyres and rims are out of the question.
* I'd prefer to stay with the 5.5 inch split rims (Now THAT narrows the available tyre field). I know some may not like this constraint, but I'm comfortable with splits and their benefits (I know this could turn into a "religious" argument). :)
* I intend to have two sets of tyres if one doesn't suit. One aggressive "Play" tyre for club trips and events, and one to do the miles as a daily driver, and probably the outback trips.

I realise that if I get rid of the splits and go to a 6 or 7 inch rim the field of possible tyres is immense, but I'd rally like to stay with the "pizza cutters" ;). I suppose if I went to wider rims I'd go 235/85 or 255/85 Coopers ST for day to day and STT for the rough stuff.