I have checked, and the prices for these fasteners in stainless steel is
higher than I want to pay.

You're being penny wise and dollar foolish. The difference in cost between the
SS and galvanized is less than you'll spend on a restaurant meal. Look at it
this way, the SS works as it should. When the kids get their drivers' licenses
you can disassemble the playset without the aggravation of rusted fasteners.
Keep the hardware for other projects, or sell the whole thing to another
generation and keep it out of the landfill.

Joe