First of all, if your old recipe works for you, why not keep using it?
In those long cook recipes they often use whole tomatos which cook down to a sauce. If you start out with a tomato sauce or otherwise prepared tomatos that long time is not realy needed.
It will give a slightly different dish, I think that is acceptable.
It may seem simple, but you must brown the mince for like 10 mins (in a separate pan). Otherwise there will be no flavour. The mince needs to go like crispy bacon. Most people just turn it over a few times and let it go "grey". The crispyness of the mince is the whole flavor.
Reducing it longer is only really fine tuning.