The repeated flushes might be more than just the toilet that is the cause. Old plumbing system (like the one in my house) are not designed to handle taking a trud from the toilet to the septic tank with just 1.6 gallons.
our old 1.6 flush toilet would normally block the pipe to the septic because the small amount of water would leave things behind.
With the new (old) 5 gallon toilet there is again enough water to carry it all down.
It must be unique to your house, because when constructed properly, the plumbing is the same whether it goes to the city, or to the septic.
When I run into a toilet that is adjusted properly yet has a weak flush, then I just tell the people that it needs to be replaced with a better flushing model.
Forty years ago people would demineralize their toilets with acid, to help restore the original flush.