In my opinion you do what you have to do, to get the results.
I've spent a lot of time in the Mary Rose storerooms while working on various research projects, and have had the opportunity to examine a large number of the shafts there. The ones that are in very bad condition and didn't preserve well are the most interesting, as the grain structure and tool marks become immediately apparent. What I realised quickly was that there is no one way of doing them. Some shafts were simply coppiced saplings and shoots that fitted the dimension specs, others were (for lack of a better phrase) "hacked" from split timber, with heavy tool marks and mistakes (just like some of the bows) and others were beautiful, carefully made and finished. Some had the slots for the cow horn inserts sawn, some were split with a blade. Some were bound neatly, some were shockingly disorganised. Some had the fletching compound applied first, some had no compound and some even had no binding or nock inserts.
The bows follow the same pattern, with many looking like your average £100 eBay job from a beginner, right up to the most astonishingly beautiful and lovingly crafted tools. I guess when you've got hundreds of bows and thousands of arrows to make quickly for a campaign you just have to get on with it. Today we're obsessed with perfect bow tillers, perfect finishes, perfect arrow shafts and straight fletchings, but it certainly seems from that one collection that back then they were focused on simply getting the job done.
The same can be seen with medieval arrowheads - some were beautiful, some were horrendous.
Personally, when I make my replicas of the MR arrows I use split timber which is then taken down with a small wooden block plane with a flat blade to the correct taper and cross section. It's a very quick process after some practice and I've done over 50 in one day before without too much trouble. Once you get into a rhythm it just flows. This method has given me results that have been placed alongside the originals and look identical, right down to the tiny tool marks from the blade digging in and the way the tapers are formed (the tapered MR shafts aren't a straight taper from head to nock).