I think it would depnd on how frquently you dispense from this keg how quickly the co2 would come out of solution. The bump every 3 weeks may be fine if you only draw a few beers a week. I am sure there are some physicists on here that could calculate the math for you, however if you dispense too many beers without recharging the co2 your beer will go flat.
I agree beergas tanks suck, refill here is $44.00. I really like my stouts and I want them on a nitro mix so I invested in a gas blender to make my own beer gas in real time. This setup is probably cost prohibitive for most, but I now pay half as much for a full n2 tank and a full co2 tank combined, and it lasts 4 times as long.