I'm sold on M4/3. Now what to get?

What you probably misunderstood (unsure) is this relation:

At shutterspeeds of 1/80 to 1/200s (give or take) shuttershock can cause the system to tremble a bit. This will be noted as a somewhat unsharp pics, also when everything is absolutely still and you have OIS and or IBIS on.
Since an electronic shutter is not a real one, it cannot cause any vibration. So when you use it, there can be no shuttershock and the pics would not suffer at all. But some cams with an eshutter (all made by Panasonic I think) drop the bitrate to 10bits vs 12bits. So if you use the eshutter in these cams, the dynamic range deteriorates. Sometimes visibly and sometimes not.
Olympus uses an EFCS (electronic first curtain shutter). It delays the real shutter by 0s (so not measurable) but you can set it to 1/8 s etc. This prevents the shock from the mechanical shutter to influence the IQ. Panasonic bodies sadly lack this. When you have a 10bit eshutter in your cam, you either take the risk of lower IQ via 10bits or shuttershock. The only other alternative is bumping ISO so the shutterspeed are > 1/200s. Which btw of course also influences IQ negatively (only from 100 to 200 ISO this will not be the case).

Panasonic went to 10-bit electronic shutter on the GH4, GM1/5 and possibly the GF7, the G7 & GX8 went back to 12-bit like the G6 & GX7 before them.

Newer/current Olympus bodies (the mark IIs) don't have any delay when using an EFC either, the delay was introduced on older bodies post-updates because apparently they couldn't simply stop the first shutter curtain from triggering, so they'd trigger it, ignore it by means of the delay, then trigger an electronic first curtain.