Even though it's been five weeks since you started this new routine, you have to remember that it has been much longer for the boy to learn this behavior to begin with.
Here are my suggestions:
1) Continue to NOT pick him up, but also continue to go down to his level to speak to him and comfort him and show him affection.
2) Find other ways to comfort him that do not involve picking him up. Maybe that means playing a game with him. Keep it positive. Tell him that you'd love to play a favorite game with him (or read a favorite book--he can sit beside you, not on your lap), but you can only do so after he stops crying.
3) Try getting him involved in calming activities. Water play is good. Get a tub, stick a little dish soap in it, and let him clean his plastic toys (the ones that can be washed safely). Clay or silly putty are calming activities, but they, like the water, are all supervised activities because the boy is so young.
4) Try some of the suggestions posted on this website: http://www.earlychildhoodbehavioralhealth.com/Articles/HotMoments.htm
--Sometimes doing something unexpected as suggested here is enough to distract a child out of his unwanted behavior.
5) Try empathizing with him. Obviously he's frustrated about something--the lack of human contact that he was getting before. I can't blame him either. It's a well-known fact that touch is an important part of human development. Continue to be affectionate towards him (keep giving him hugs, even if you're not picking him up anymore). When he's screaming, tell him, "I know that you feel sad because Mommy/Daddy isn't picking you up anymore, but I still love you very much."
6) Encourage him to use his words whenever possible. This will help to cut down on some of his frustration levels.
7) Try making him Mommy's/Daddy's little helper. Spending more time with him, doing things together serves two purposes: a) it gives him that human contact he craves and is used to, and b) helps him to learn to become more independent.
8) Praise him whenever you can.
9) Try to use humor whenever possible. It relaxes the body and relieves the stress that everyone is going through.
10) Try to do more physical activities with him. Do a little dancing to music or running around or whatever he can do physically. This should distract him and use up some of that energy he's using for screaming.
Hopefully one of these things (or all used together) will help you resolve your problem.