It doesn't really matter when you cut the excess stems back. You'll be repeating the operation for ever because hazel wants to be a multi stemmed shrub. As well as the nuts it is that genetic predisposition to produce a constant crop of straight rods which has made it a boon to humanity for building, weaving, fencing, firewood etc over the centuries. I've trained a wild Corylus avellana to be a small tree, just out of interest, but it never produced a really solid central trunk like a crab apple. You'd need to stake the main stem to keep it vertical. But if you want an honest opinion I wouldn't bother.

Corylus colurna is an attractive, genuinely tree-form, hazel species which is often seen as a street tree over here. I don't know if it would grow where you are.

Hmm, that does put a bit of a damper on the train into a tree idea. Somehow I guess I assumed that at some point it would stop putting up new stems. I'll have to think about it though. It might not be that big of a deal. The nearby crab apple trees produce numerous suckers and I find myself trimming them away all the time. It probably wouldn't be that big of a deal to add two more trees to the sucker trimming.

If you do a bit of googling on 'hazel coppicing' you'll find info on how hazel has been used as a valuable crop for centuries by virtue of its production of suckers. They are a very different phenomenon to the odd sucker you might get from a crab apple. I have wild crabs in my wood and they are all naturally trees. I have thousands of hazels and they are all stooling shrubs. They never stop putting up suckers. Also if you are growing them for nuts why cut off the majority of the fruiting stems?

You could do an experiment by digging out and replanting one stem with some roots and starting to train it by staking it and removing any new growth from the base.