We started leaving the crate door open for Henry at night 3 weeks ago (at 5.5 months), and his sleeping has improved so much! It was something we always struggled with - the little chap waking me up (with a little whine or bark) at 5.30 or 6.30 or 7.30 if I was lucky. Since we left the door open he just comes out and potters around, plays with his toys, and sometimes I even have to wake him up now (the latest has been 8.45, even after the clocks going back!). At the same time we've started leaving him during the day, not in the crate. We never managed very well with crate-training him during the day - he was fine if he was really sleepy but if not he'd whine and bark and sometimes wee. We were a bit worried about separation anxiety. Once he'd started sleeping outside the crate we thought we'd leave him during the day, and used a camera to video him a few times. Basically, he whines a bit, potters around, and then eventually just goes to sleep. Within a week we'd gone from 15 minutes to 3 hours, with him being fine. We have an open-plan sitting room/kitchen, so he has the run of this area (the only other area in the flat is the tiny hallway, bathroom and bedroom, which he's not really allowed in anyway).
Obviously it depends on the dog, but this method worked for us - starting with an open door overnight, and moving on to leaving him uncrated during the day (and we don't give him a kong either). The crate is still there, and he sometimes wanders there in the evening, and sometimes I find him in there in the morning.
We're off to stay with friends on Saturday night, and not taking the crate, so it'll be interesting to see how he gets on in a strange house (a bit worried that he might scratch the doors, but since he's never done that here I think he'll be fine).
I'd start with overnight and then short periods during the day, but tape him to see what he gets up to! Does he normally hang out in the kitchen? Is there somewhere comfy for him to sleep?