I don't know the icumed from the top of my mind but IBP transducers usually have a pinout where the excitation and signal lines are "intertwined" like supply+ signal- supply- signal+ or similar, but the supply together and signal together looks very wrong to me.
Between the suppy in pins you should measure a higher (>1k-ish) resistance than between the output pins.
When applying power supply, the signal lines should be close to 1/2 supply voltage relative to ground.
Consider adding at least some capacitor between the Instrument Amplifier reference and ground, they like lower impedance here. That nice schematic in the datasheet, where the offset compensation voltage is buffered with a OpAmp, is there for a reason.
Good luck!
Hendrik