Their solution as a nothlit was their half way option between just killing him and letting him run free.
And really, the only reason why they never killed him was because he was human.
If it were up to me (or Rachel), I would have forced a confrontation; battle morph against battle morph. David goes Lion, I go into presumably an equally strong animal; perhaps a Bear. Bear against Lion, I'd make short work of him. If he managed to take me out some how, there's 4 others who could take him in a morph, and Ax could have taken him out easily.
If he tries to demorph to take advantage of my morality and refusal to kill a human, I calmly put one claw to his neck and kill him if he continues demorphing. So basically, force the fight to the death. If he tries to demorph to heal his wounds, he dies there as well; a dead lion.
If I had to trap him in a morph, I would have him trapped in another human; one who was born blind and mute. Since human morphs can't thought-speak, David can't see or speak while trapped. He can hear everything, see and say nothing, nor betray his secret (or the animorph's). To ensure that the two hour time limit passes, I need merely sedate him. By the time he comes to, it'd have been too late.
Alternatively, he could just be forced to morph into a mute person; subsequently, sedate him and then while sedated, remove his eyes. Unable to speak, see, thought-speak, and trapped in a morph, he'd be well-cared for in society by many many groups who help the needy. He wouldn't even have to fend for himself. It would be a very simple life; one where you are fed and hydrated day by day, have a place to sleep, but cannot see, nor speak.