Thank you! Turns out I forgot the normalization constraint and might've initially misinterpreted the part about the continuity constraints (it is actually 2 at each boundary, not 2 in each interval as I initially thought).
For the case of general potential V(x), what does it mean when he says that there are always one more constraint than free parameters? At each interval, ψ and ψ' must be continuous, so that is 2 constraints at each interval, and I understand that there are 2 parameters of the wavefunction in...