IMO/IME, WAIT until the brew is ready to drink before you keg it. The only thing missing should be carbonation. Kegging green beer, carbonating it in the fridge/keezer/kegorator will give you carbonated, slightly less green beer. Carbonation time is NOT the same as bottle conditioning time due to the temperature differences. You bottle condition at ~70F for 3+ weeks. You carbonate, at serving pressure and temperature, for two weeks. At the lower temperature aging/conditioning happens MUCH slower.
I would wait until the brew tastes like you want it in the glass (sans carbonation and what it brings) and THEN keg it up and put it to serving pressure (once it's chilled of course). If you plan on leaving the brew out of refrigeration, then you could count that as conditioning time. But, IMO/IME, you're better off not.
For reference, I use 3 gallon kegs, getting 6 gallons out of primary (so filling two) for my normal size batches. One goes into the brew fridge as soon as a spot opens up, the other is saved for later on. I leave my batches in primary for 3-4 weeks for my normal batches (usually the OG is over 1.060), with bigger brews getting longer. I have a batch that was probably done fermenting in the first week, but it won't be kegged until either this weekend or sometime next week (it will be 3 weeks on Saturday).
As for your desire to rush a batch through... DON'T!!! Also, 4 days in primary and 5 weeks in keg (in the fridge) is NOT the same as 3 weeks in primary and two weeks in keg (carbonating)...
Also, have you taken a SG sample/reading since you think it's done fermenting?? Take another about three days from this one and compare. IF it's a 100% identical reading, chances are fermentation is finished.
As for your desire to brew another batch... Get more primary fermenters. I have three for my normal size batches, one for a 10-12 gallon batch, soon to have another for my normal size batches, as well as smaller ones for meads and such. Right now, I brew once a month, but I can easily handle twice a month with the fermenter count. I'll be able to do every weekend once I get my fourth fermenter finished. A twice a month brewing schedule can be challenging, when you have other things you need to do on weekends too.
Basically, give your brew the TIME it needs/deserves to become the best it can be. Otherwise, just go an buy a case, or keg, of BMC...