Actually positive / negative feedback is a very unhelpful way of looking at the situation. Its a classic energy balance emergent system. Overall input energy has to equal output energy and for any input energy level a simple vector can be derived to track the cloud cover variation needed to achieve this. Only needs a grey body source model at both ends. The problem is of course that locally its not a pure radiative source / sink situation so for accurate results you need to track the energy vectors of everything else that's going on. Like wind which transports energy horizontally. However in principle its possible to generate a vector array as large as you want and as accurate as you want.
Of course being an emergent system you can't calculate the thing and pin it down on a map. Only way to get the answers is to run it and see. This is a job for analogue computers, or the functional equivalent, not conventional digital machines. Computing section where I worked had a combined analogue and digital machine which was very impressive on the right jobs, easily outrunning a triplet of PDP 11(?). A modern, all digital, development would be ideal here.
Nice thing about emergent systems is that, for small changes at least, exceedingly crude models can generate a sufficiently accurate vector to track enough change for the job. My HP67 was good enough to figure out 0.1 °K target temperature changes when predicting IR imager performance! Its a trivial matter to demonstrate that the cloud feed back loop has ample stability margin to kill off any possible CO2 induced changes however calculated. An irrelevance in practice given that the CO2 band transmission length is at best, about half the height of the troposphere so CO2 changes can't have any effects anyway.