But it takes so long to evolve

I don't see the problem. There is no simple dichotomy between living in and out of trees. The average domestic cat is not basically arboreal like a monkey but can scoot up a tree to escape a dog quickly enough.So maybe your "ape-man"'s ancestors start by spending a little more time on the ground. As time goes on they start to venture out of the forest on short expeditions. The expeditions take more and more time and they take advantage of small stands of trees outside the forests.There's no need for a sudden move. Just a gradual change of lifestyle.

Looking at the points raised.1) Yes you can get a new species in 100 years but it won't be very different from the species it branched off from. If you're lucky there might be a superficial but obvious difference - but on the other hand it might be distincuishable only by breeding experiments.2) Sudden changes of environment are not good - if a species is not well adapted enough to make a living in the new environment it will go extinct (and how well adapted that has to be will depend on the competition).3) Gradual changes of behaviour - slowly moving into a new environment will still making use of the environment the species is moving out of are easier to handle. The creatures still get some of the benefits of their existing adaptions but also experience a selective pressure to do better in the new environment.So there is no one answer. Assuming that the new environment is different enough to require significant physical changes to do well the options are really down to slowly adapt (although that is probably hundreds of thousands of years rather than millions) or (relatively) quickly die out.