I would advise to do summer pruning rather than winter pruning, preferably after the longest day, as the tree will then show less of a growth reaction, meaning less
water shoots.
And prune only little off at any time, not more than 20 - 25% or so, otherwise you'll get the same reaction problem. The pruning you're facing now could be the result of a previous pruning exercise. Usually, once you start pruning, you end up continuously pruning, as new shoots which are the result from pruning will often grow in undesired ways. This does looks like a strong grower, so then it does need some
freedom to grow.
A central leader approach seems wise to me, that's also the way this tree would want to grow naturally, so that'll give you less problems.
I find it hard to say where I would make cuts, I find that already hard with my own
trees, and you do have good ideas yourself about what you want and don't, and you see the whole picture.