Am I correct to assume slack tyres bad for fuel economy, well-pumped hard tyres good for fuel economy?
Yes. lower pressure increases the rolling resistance of the tyre (like trying to roll a squishy pillow). Higher pressure can lead to a harder ride and a tendency for the tread area to get more rounded (like a cycle tyre) which can reduce the area in contact with the road and concentrate tread wear along the centre of the tyre.
A couple of extra psi should be ok but I wouldnt go higher.
But bear in mind that tyres can lose 1 - 3 psi a month due to air permeating through the rubber naturally
(not a leak as such) so check the pressure regularly. Also note that tyre pressures increase as the tyres warm up as you drive. So if you drive to a filling station and put 32psi in , they may only be at 30 psi after they have cooled down overnight..
Also check the accuracy of the tyre pressure gauge you use by comparing it with another gauge (or two)
Do both measurements at the same time so you are comparing like with like. If you drive home first or compare them next day tyre temperature can affect the readings - Gauges can be inaccurate by a few psi. You might think you have 32 psi but really only have 30 psi , or 34 psi.