Now. Now. Now...... you are in a window and it is rapidly closing. In a couple of months he will be too big for the swing to swing correctly and you will be up that creek looking back at a paddle! As far as making the transition easier; put the swing in his room first. Take the first nap in there in the swing in his DARK room. If he sleeps well, go on to the next step. Second nap, swing in dark room until he is asleep for about 15-20 minutes and then move him to the crib. He will probably wake up during the transition, which is OKAY. He'll be so drowsy he'll probably fall back asleep. Do this for a couple of days until he's fine with it, then move to step 3. Swing for a couple of minutes until he is drowsy but still awake. Move him while drowsy to the crib. Do that for a week or so, then try looking for the drowsy cues before you would have put him in the swing. Then try putting him straight into the bed and turning the swing on (so the familiar noise,etc can soothe him).
Your son is capable of sleeping through the night. You've said he does it. Now all he needs is some help to learn to self soothe, and you're set. You can do it but it might take some hard nights. In two weeks you can be free. If you don't do it now, you'll be stuck because at a certain point, they get too heavy for the swing to be satisfying. Then you end up trying to put the crib up on those vibrating step things - which can be a last resort if the above doesn't go well....