There are two limits to how much power a regulator can handle
a) Its data sheet max current and max power handling
b) Its heatsink capacity. You'll notice on that diagram, it says 'with Heatsink' next to the regulator.
If you read the data sheet, you will see that the max power handling is dependent on you keeping the case temperature low enough. If you don't have an adequate heatsink, the case temperature will rise. Fortunately for you, the LM350 is internally limited, so that before the temperature becomes dangerously high, it stops regulating to protect itself.
If you want 1.7A at 12v out, that's around 13 watts being lost in the regulator (voltage drop * current). That's going to need a significant heatsink. Look in the data sheet to see what the max case temp is allowed to be for 15 watts, then pick a heatsink with a thermal resistance that will keep it to this temperature in your ambient. You will need to do some sums, but fear not, thermal resistances add up like resistance. If you take heat flow as current, and temperature difference as voltage, you can apply a thermal 'ohms law' to the sums.