What happens if you do a 'sudo modprobe i2c_hid' from within the live environment? Which iso did you try exactly, 18.04 or 18.04.5? Can you also check with the latest 'ubuntu-20.04.2.0-desktop-amd64.iso'?
So the working solution pulls in hid_multitouch when inserting i2c_hid, the non-working does not!
The log from Xorg.log when working is:
[ 130.980] (II) LoadModule: "synaptics"
[ 130.980] (II) Loading /usr/lib/xorg/modules/input/synaptics_drv.so
[ 130.982] (II) Module synaptics: vendor="X.Org Foundation"
[ 130.982] (II) Using input driver 'synaptics' for '0X45 0X4C 0X41 0:00 04F3:308C Touchpad'
[ 131.020] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: x-axis range 0 - 2943 (res 31)
[ 131.020] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: y-axis range 0 - 1747 (res 32)
[ 131.021] (II) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: device does not report pressure, will use touch data.
[ 131.021] (II) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: device does not report finger width.
[ 131.021] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: buttons: left right double triple
[ 131.021] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: Vendor 0x4f3 Product 0x308c
[ 131.021] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: invalid pressure range. defaulting to 0 - 255
[ 131.021] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: invalid finger width range. defaulting to 0 - 15
[ 131.021] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: touchpad found
[ 131.076] (**) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: (accel) MinSpeed is now constant deceleration 2.5
[ 131.076] (**) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: (accel) MaxSpeed is now 1.75
[ 131.076] (**) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: (accel) AccelFactor is now 0.058
[ 131.077] (--) synaptics: 0X45 0X4C 0X41 0:00 04F3:308C Touchpad: touchpad found
The non working looks like:
[ 4.477] (II) LoadModule: "synaptics"
[ 4.477] (II) Loading /usr/lib64/xorg/modules/input/synaptics_drv.so
[ 4.478] (II) Module synaptics: vendor="X.Org Foundation"
[ 4.478] (II) Using input driver 'synaptics' for 'ETPS/2 Elantech Touchpad'
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: x-axis range 0 - 2943 (res 31)
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: y-axis range 0 - 1747 (res 31)
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: pressure range 0 - 255
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: finger width range 0 - 15
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: buttons: left right double triple
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: Vendor 0x2 Product 0xe
[ 4.502] (--) synaptics: ETPS/2 Elantech Touchpad: touchpad found
[ 4.521] (**) synaptics: ETPS/2 Elantech Touchpad: (accel) MinSpeed is now constant deceleration 2.5
[ 4.521] (**) synaptics: ETPS/2 Elantech Touchpad: (accel) MaxSpeed is now 1.75
[ 4.521] (**) synaptics: ETPS/2 Elantech Touchpad: (accel) AccelFactor is now 0.058
[ 4.521] (--) synaptics: ETPS/2 Elantech Touchpad: touchpad found