You want to put ointment directly on the feet, a little goes a long way. I'm not sure where you are looking for bag balm, but I got my 10oz tin for about $15, most hardware stores sell it in the farm animal section. That doesn't seem that bad of a price, though I guess Vaseline is cheaper, but it doesn't contain the antiseptic like the bag balm does. A better option then Vaseline though would be vitamin E, you can get the gel caps at a drug store and just poke a hole and rub the oil into his feet.
The best way to apply ointment is to gently hole the chin by the base of the tail, as close to his butt as you can. Lift his back legs off the ground and use a q-tip or your finger to apply the ointment to his feet and rub it in. If you have a second person there it makes it a lot easier. You want to rub it in as best as you can (like putting on lotion) and as I said a little goes a long way you don't want to leave a glob on this feet.
Keep in mind though that chins are not suppose to have soft feet. Kits start out with soft feet but they are suppose to develop tough calluses on their feet as they grow up, it helps protect their feet from injury like shoe soles. So you don't want to soften the feet too much, but they should not be cracked or peeling either.