OK this should not be that difficult. Trying to diagnose stuff like this over the internet, sight unseen, is probably stupid, but then that's right up my alley.
Depends on your position. It sounds like you're just doing everything from standing position. In this case, it should be a matter of figuring out what technique(s) works best for you. First, I would try moving the front sling attachment point further aft. This should give you more sling. If not, get a longer sling. Loop it left or right; see what works best. Then look at what you need to do to take up the rifle weight. Armpit tuck, elbow tuck, whatever, figure out what works for you. Look at which position works the best, as far as where the rifle is when you reload. Try and get it up as much as possible in the "work space" so you can keep an eye on things, but get it where it needs to be so you can reload. Grab the mag, push/pull like others have said. It just sounds like you need to quit worrying about how everyone else does it and figure what works best for you.
Kneeling. A little easier here since you have better support. You can use your chest more to help steady the rifle while you switch mags.
Prone. Can be harder, but, since you're using a chest rig, should be OK. May have to cant the rifle more to insert mag.
Sometimes I just loop the sling over my neck and go from there. Easy to loop an arm in for travel/whatever when necessary.