I sympathise, I've been there. Also have a very nervous dog, and he cried piteously as a puppy, when ever I was out of sight.
This is what worked for me:
Yes, cover the crate during the day. It needs to feel safe and den like, so only leave one side open. He will be reassured nothing bad is going to jump on him from behind. If you have a cubby hole, or under work surface knee hole for the crate, even better.
Establish a routine, where he is on his own for certain periods every day. I did this from day one, and within a few days the crying diminished. If you are with him 98% of the day, every day, he is going to develop long term separation anxiety. Try putting him in his crate when he is tired after food/toilet/playtime.
The five minute thing didn't work for me either btw. Going for a routine did, but it did mean a few days of being yelled at (I'm suspect I will be shot for this....)
Water in the crate, always. If he's crying he'll make himself thirsty, and if there is no water he'll cry because he is thirsty.
Leave the radio or TV on.
Hover outside the door if need be, and only go in to him when he is quiet. He will pause occasionally.
When you come in, don't look at him or go to him until you have sorted yourself out - hung coat up, put bag away etc. It just helps to reduce mad hysteria over 'mummy's home'.
On a different note, if he is nervous go OTT on the socialising with other dogs, not just at classes, but out and about. Mine has developed nervous aggression towards other dogs and that is a much tougher nut to crack and crying!!!