No problems at all.
Make sure the tank is high enough and tyhe carb will change position. Better still, buy a pump or regulator and get the tank over the CG. Start the engine with the aeroplane inverted.
Just make sure you have controll of the cooling. The two openings at 9.00 and 3.00 oclock on an Extra cowl aint' going to cut it. Better to leave 'em uncut or block them off... and make/cut/design and new set of openings at the bottom.
Remember the outlet area needs to be 3x the inlet area.
95% of people having problems running inverted engines and track the problem down inadiquate cooling and/or/ tank position.