You are indeed correct my POH does approve the use off left and right positions, but it also makes it clear this is unusual and points out that you may have to use the fuel pumps to restart the engine when it stops due to fuel exhaustion.
I really see no benefit in changing tanks on a fuel system designed to be drawn from both at the same time. Why do you need to know how much fuel is in each tank when you draw from both tanks? It makes no difference that the fuel draws slightly unevenly as Cessna tanks are designed so that in the both position you can empty one tank without problem.
You are as usual coming up with a solution for a problem that does not exist.
We do not expect a PPL hirer to check the AD status, we expect the hirer to ensure that they have access to the POH and that that if they old and faded fuel switch placard is unreadable that it is replaced. We don't expect you to have to make stuff up to fix an imaginary problem.
Edit to Add:
SNS is absolutely right, I said the same thing a few posts ago. Read your POH and operate accordingly. Don't make up stuff ala DFC style.
Personally I use a fuel computer linked to the GNS430 and fly with both tanks on. Over thousands of hours it has proven to be accurate to a fraction of a litre (usually the fractions drained for fuel tests and fillinng my tug!)