Robert:
Friction only approaches unity for dry rubber on concrete / tarmac. As you say, other surfaces (grass, dirt) are considerably less. Just keep away from areas with severe sinkage - it's too difficult for a light-powered machine.
As you have deduced, debris is a real problem. On sand or gravel, the spoil is carried on the track like a conveyor belt and interferes with the drive system. On an excavator or a tank with lots of power, it is simply squeezed out of the way. Fist sized rocks are crushed to powder by the steel tracks and the huge amounts of tractive force available. Skeleton track obviously helps as it provides an escape route for the debris. But this is a difficulty with rubber belt tracks and low power.
You have two requirements for the track drive system; one is to guide the track over sprocket, idler and road wheels (and return rollers if you have them) without rolling off the side. During a neutral turn (pivoting) there is of course a huge side force on the track. This is reacted on a tank by a spike or 'horn' that projects inwards from each track link, which engages with a groove in the rotating components. On a belt drive, you can use side plates on the rotating bits to keep the track on, but they do tend to get blocked with dirt, damaged by impact, etc.
The second requirement is to transmit torque; this can use the horn but usually relies on a hole at each end of each link which is driven by teeth on each edge of the sprocket.
Look at the Diehl (German) website to see some typical solutions.
Unless you have a large budget, you could find a suitable size industrial timing belt and ask a local rubber company to modify it for you with some sort of drive / location pegs on the inside surface. They would have to vulcanise these onto the belt - not sure how durable this would be. You might even consider fixing a series of metal or plastic (acetal?) cones on the inside using countersunk bolts from the outside.
If your drive components are timing belt wheels, you could machine relief grooves and/or holes in the running surface to allow debris to escape. Your belts will be sized for ground pressure considerations not torque transmission so you can rely on less than the full quota of drive tooth engagement.
John