PPonting
It is the school's aeroplane, so I guess that they can dictate SOPs.
However, I have done most of the things that you mention with pax in the back, during training and that obviously was not considered a problem by the school I was flying with.
I think that your idea to fly the PA28 at heavy weights is sensible - it does handle a little differently, although not dramatically so. Also, the 850fpm rate of climb that you could get out of a lightly loaded Archer will be reduced to crica 500fpm and it is no bad thing to experience that under instruction, before you go out alone.
You will find, in general terms, it is rather easier to handle than a Tommy and is a very docile platform for touring.
I disagree, respectfully, with Beechnut. No observation for low hour pilots is ever a waste of time, there is much to be learned from watching others being taught.