All the coverage so far has focused on instrumentation. Will the LAA also have stability criteria?
Yes. See section 3 of
http://www.lightaircraftassociation....assessment.pdf
Some of the LAA approved models already have restricted aft CG limitations for instrument flight, due to handling issues.
It is far more important for an aircraft to be a good 'instrument platform', with reliable 'blind flying' instruments than it is to have all the latest toys from the avionics manufacturers....
Some of the early wartime fighters were pretty awful 'instrument platforms' due to their stability characteristics and instruments. Luftwaffe pilots sometimes preferred to spin the Bf109 down through clouds (assuming the cloudbase was known), as that was a known manoeuvre which got them down more easily than risking losing control in IMC.