wow, thats an interesting problem!!!

i think the best way to train him would be to take a few days off of work, or adjust your schedule (s) so that someone is always around when he gets the urge, so you can correct him. he probably doesn;t know he is doing anything wrong, and he doesn't need to go when you let him out because he goes when you leave ( my dog did the same thing)

i have a couple questions that may help us help you.

1. what kind of food do you feed him? you mentioned his stools were usually loose and infrequent. and do you feed him at regular intervals or just keep his bowl full?

2. have you taken him to the vet to rule out any health issues?

3. how big is the crate you keep him in? he shouldn't have enough room to move around enough to go potty without standing in it.

i used to leave my dog in the kitchen ( tile floor ) and there would always be a minefield at the far end when i came home. i started putting her in a cage that came with a divider so you can increase/decrease the amount of room they have, if its too big then they will just go in the corner and still have enough room to not lay in it. may sound cruel but trust me its not, and it works.

also he is probably bored, do you give him plenty of things to chew on?