The first stage doesn't serve a meaningful purpose in your design. Would be different with non-inverted buffers or a differential stage as used in the classical three OP instrumentation amplifier, usefull if you want high input impedance.
I forgot to mention that + and - inputs have to be switched for the single OP circuit.
The original circuit lacks of a suitable bias. It could be fixed in a different way, but you need to connect the non-inverting OP inputs to a positive voltage instead of ground. But as said, this would be purposeless effort.