Sounds similar to some of what use now and in the past.
Here's some things you might want to consider or think about.
The way i figure at a 2 gal/hr refresh rate it will do roughly a 50% water change every 72 hrs.
It doesn't work that way (don't worry I had that thought before too)
Since you have a constant filling and draining - new and old water mix then the mix goes into the drain.
Think of it like you have a two liter pop bottle 80% full of red water,you add blue water = the excess that slips out - won't be red it'd be purple. - Same pricipal for a tank except theres more to dilute.
It doesn't matter if it's not 50% but if your trying to change 50%
(like a 50 water change) you'll need ALOT more incoming water
The temp
Temp shouldn't be a problem - but if you can't match the incoming water to the temp of the tank - use cooler incoming water -It's alot easier for a heater to adjust for .5% of cooler water then it is for the fish to adjust to higher temps or temperature spikes.
I know you said you were going to use valves
Once I get it set by adjusting each where I want them it should stay regulated.
Again - same thought I had before ,if you live alone it'll be fine but if you live with other people - showers,washing dishes,laundry etc.. can change the temp even after the valves - thats why I now use slightly cooler water.
Any uneaten food or film should go into the overflow which will have a drain attached to the house plumbing.
Doesn't work

- A water change system is great for HELPING keep a tank clean - but you'll still need to do regular type water changes and Vac.. the gravel. Regular water changes won't need to be done often but they'll still be needed.
I say gravel vac.. still needs done because - All food that sinks,avoids the overflow and most fish waste will also sink and avoid the overflow (even in a bare bottom tank).
adding 2gph though definately won't cause a problem on a 300 gallon tank - it's only a .5% (or less) addition/change in an hour
There's no maintance free way to keep a tank - I've tryed everything
