dunno about other tyre shops but my dads tyrepower charges $5 per tyre to dispose of them as it costs a lot these days, have to use a licensed disposer n shit. if you buy new tyres the fitting, balancing and disposal of old tyres is all part of the cost of the new tyres.
cant remember what he charges for changeovers but when it comes to small jobs like that, cash is your friend
and the tyre shop was right, low profile tyres are a fair bit harder to change without the right machine. even with the right machine if they're upside-down rims, they're a prick to change.