Having been in those conditions, your one saving grace is that the air is relatively dry during that time of year, but the sun load can really make it tough. Some things you can look at is ensuring the system is properly charged, and that the evaporator and condenser are free of debris. Ensure the ductwork is all hooked up, and that your blower motor is operating at full steam. Easy upgrades can be sourcing a larger condenser (make sure you get the right type depending on the refrigerant you're running), and perhaps converting to high-flow electric fans for the radiator and condenser. You're still fighting a losing battle, though, as the system that was adequate for a pickup truck isn't going to be as effective cooling the large cabin of a Blazer.
A Vintage Air kit or similar will fit with minimal modifications and features more efficient and more modern components, and will likely cool somewhat more efficiently but at a price. Some have looked at the more complex (and pricey) method of adapting the rear cooling system of a Suburban or one of the aftermarket add-on cooling units.