I would start by doing research on any names or markings to see if this was a mass produced item or a one-off. If you find examples of other planes by this maker it may help you determine which parts were original. It might also help you determine if the plane is rare and valuable which would probably mean that you would be better off selling the plane to a collector who would probably want to preserve it as-is, and using the proceeds to purchase other tools. You stated that the screws were replacements and I wondered if you deduced that from any countersinks on the plane body that would indicate that countersunk screws were originally used. If the plane was “shop built”, it could be that the original maker didn’t intend for it to be used for shooting so that smooth sides became a moot point in the construction. If there are no countersinks present then the original maker probably never intended it to be used on it’s side and that may mean that the existing screws or similar screws were originally used. The sides appear to be rather thin and I question the idea of introducing countersinks just to smooth up the sides for shooting use. The idea that it is “shop-built” might also explain the mixture of woods present, as well as the “less-than- perfect” previous repairs.
If you determine that this is rather common plane of little collector value, then it sounds like you are on the right track in general and any “repairs” or “improvements” would strictly be based on your judgement. I personally would try and repair the existing knob and handle and try to find a piece of rosewood, or at least a similar wood, to replace the de-laminating section.
Anyway, it sounds like a wonderful project and I hope you will share the finished results with us.