I have tried holding the float down to allow the tank water level to raise
to the waterline mark (which takes the water level over the top of the
inlet valve) - this produced a more significant flush which took away the
toilet tissue, but I doubt that it would have taken away much else.
Snipped

I think the fact that you are using old and new 'technologies' is the issue.

I suggest that you raise the water level to where it should be and then
think about changing to a new WC and cistern.