However, one of the other requirements is that it must be able to fly inverted for 4s without load.
How should this impact my choice of aerofoil, is at all?
I'm going to assume that "without load" means "without payload", not "in a zero-G condition".
I'm going to also assume that there is no requirement that the altitude be constant during the inverted segment-- i.e. I'm going to assume that descending flight is allowed.
If so, the 4-second inverted requirement should have no effect on your airfoil choice.
As a strategy to intentionally lose altitude, I've held a "E-flite Radian" radio-controlled motor glider in unpowered (descending) inverted flight for literally minutes on end. The Radian has an undercambered airfoil that is far from optimal for efficient inverted flight. Yet the resulting best glide angle in unpowered, inverted flight is still relatively flat (perhaps 10 to 20 degrees below horizontal?)
Your primary issues in a brief segment of inverted flight will revolve around structural integrity and controllability (especially if the wing has dihedral, which degrades controllability in inverted flight), not airfoil efficiency.
(Hint: don't assume that the requirement to demonstrate inverted flight rules-out a no-aileron design, with ample dihedral, and with rudder and elevator as the only control surfaces. Such designs can in fact be flown inverted for prolonged periods by a proficient pilot, so long as the rudder is sufficiently large and has ample throw.
The "Radian" glider mentioned above, when set up optimally, is an example of such a design.)
In fact my recommendation would be the same even if the requirement were that the aircraft must maintain altitude while inverted, with zero payload. Back to the "Radian" motorglider as example-- despite the undercambered airfoil, it is perfectly capable of a modest sustained climb rate in inverted, powered flight. So design the airfoil for efficient sustained upright flight with the required payload, not for the brief no-payload inverted segment.
Another note-- depending on the exact rules at play, and the discretion of the judges, you might consider doing the inverted section as part of loop. Would the judges count all portions of the loop where the aircraft was even slightly inverted, as contributing to the required 4 seconds? If so, depending on entry speed (the higher the better), it seems quite possible that you could meet the 4-second-inverted requirement with the G-loading (and therefore the lift force) never even going negative at all, or only going slightly negative for a brief interval.
Another way to show how much you can "get away with", for brief intervals of time, in terms of non-optimal airfoil choices, is to take a radio-controlled model airplane with flaps and experiment with sustained inverted flight with the flaps down. You might be surprised at what is possible! Design your airfoil for the main mission, not for the 4 seconds of inverted flight.