700R4 is a 4 speed version of your 350. A very good unit and with some minor upgrades it will last you a long time.
First, you need to be sure that you can add the trans downshift cable to your carb. If you can get the bracket off the donor it will make it easier. The cable is self adjusting if you follow the directions for the donor vehicle too.
Upgrades I would absolutely do before installing are a deeper pan to hold more fluid, preferably with a magnetic drain plug. Be sure to install the spacer for the filter so it can pick up off the bottom of the pan.
Next I would either bypass the radiator trans cooler all together or run inline with a PLATE AND TUBE trans cooler. DO NOT get one of the tubes with the foil fins on it, they aren't nearly as efficient. Get the biggest one you can find. My 85 K-10 has one for a 26,000 pound truck that I grabbed at a chain store for less than $50.
Lastly, since you are going all out here, add a temp sensor and gauge to the OUTPUT line from the trans to the cooler. This way you are getting a true reading for the fluid in the trans. If you can find a deep pan with the port, install the sensor there. If the fluid ever gets above 260*, change it asap!
How did I learn all this? Why, I blew up my plow rig of course! Now I have a rebuilt trans and all of the trimmings. I have plowed 4 years with it and had not a hiccup since. Good luck!