On the Sabre 456 (a sloop), they had it rigged with a self-tacking jib. This would probably work well in place of the genny on cutters. I'm just not sure how efficient that sail setup would be though.
Invariably, using a staysail, no 'headsail' and full up mainsail will result in heavy helm problems (weather helm) ... on most cutters, for neutral helm or minimal so called 'weather helm' when flying ONLY the staysail + main .... its usuallly also required that the mainsail have at least have ONE reef in so that the sail plan is 'balanced' with respect to 'weather helm'. You reefing sequence for a cutter rig - "back to front": main, then headsail, then staysl. Most (true) cutters will sail along nicely on just a staysail because the CE is usually in front of the mast and IN the staysl.
If one sails with only the staysail and a *full up* main, you usually wind up dragging the rudder somewhat sideways to compensate for the developed 'weather helm'.
You can use this two sail combo (with full up mainsail and staysl) but it almost requires that the main be cross-cut woven dacron and the main be shaped 'board flat' by the outhaul, and with extreme main halyard tension
to relocate the point of maximum draft in the main well forward of 'normal'. The problem with this extraordinary 'shape' is that a 'flattened' sail is a speed shape
for sailing in 'flat water' and will be 'lousy' for 'blasting' through high chop or high waves where a full drafted shape is needed to provide the 'power' (second gear).
BTW ... using a BIG genoa 'over' a staysail is of little aerodynamic benefit when 'pointing', as the leech of the genoa HAS to be 'ahead' of the leech of the staysail for any aerodynamic advantage ..... when 'pointing'. Using a BIG genoa 'over' a staysail when 'pointing' probably has only a slight advantage of reducing mast turbulence and flow over the mainsail ... and not much more than that and only at 'moderate wind speeds'.
Sailing a Cutter rig is VERY different than sailing a sloop ... the aerodynamics are quite 'different' and it really takes a bit of time to get it right.
JeffH usually recommends a fractional with big mainsail ... except for downwind or broad reaching, I might agree with him due to the 'overall versatility' of the frac. rig over a cutter rig.