Can I split a shared neutral between two GFCI breakers?
Can't do that.
You need a 15A 240V GFCI breaker (takes two spaces, one handle, two hots, one neutral) to pull that off.
A shared neutral is only feasible if the GFCI can look at both hots and the neutral to detect differences. Two separate 120V GFCIs cannot do that. One 240V unit can.