We used load cells at work so I have some experience with them and have a few pointers and ideas you should consider.
First you shouldn't try and build-in perfect calibration via the op-amp gain, just too many causes of drift and application requirements. It's better to build in a zero, and/or tare function in your software. Tare is the term they use when you want to weigh something that is in a container but only want to know the weight of the material, not the material + container weight. This effectively means you don't require perfect zero bridge output value, just have a software function read a user switch or control to tell your system to use whatever analog voltage it is seeing as the zero value. For gain you should have a calibration function where after you zero the system you place a known calibration weigh on the cell and again have a switch or control to tell your system it's maximum analog input voltage. After that it's a simple map() function to determine the unknown weight to be measured. You could store these bottom of range and top of range values in EEPROM memory if you don't wish to 'calibrate' the system with every use after powering off. I'm probably not explaining this that well, but you are bound to be disappointed if you just assume that the initial zero and gain values set externally by your load cell and op-amp will hold accuracy over time and temperature.