Just a quick note - and I'm by no means an expert so take this with a pinch of salt but I've encountered this issue when working on warbows myself - when you say the big warbow is using Mary Rose dimensions, does that mean you took your unworked stave, and drew out the profile of a finished Mary Rose bow on the front and sides, then cut to those lines?
The reason I ask is that I've tried that before, and what tends to happen is that the tips are always way too thin and narrow early on. If you rough out an untillered bow to the exact dimensions of a finished bow, the tips will of course be tiny in comparison, and all the stresses and strains of tillering will be focused straight onto the tips, rather than the whole bow. This leads to hinges and whip-tillered bows instead of nice full compass shapes.
If you're working to a Mary Rose bow as an example, cut the front profile out leaving the tips fairly wide - say 20 - 25mm instead of the 12mm on the finished bows, and much thicker than the bow you're copying. Tiller the bow so that the tips don't even start working until it's 90% finished, then narrow and thin the tips down to get the limbs to complete the full compass. This will avoid any nasty hinges and whip-ends which you may be encountering by trying to copy a finished bow.
The reason the tips on warbows can be so thin is that by the time they're reduced the rest of the bow is already doing a lot of the work, and the wood has been taught to bend and stretch and share the strain. At this point, the tips don't really take much more stress, whereas if the bow is huge and untillered, but the tips are almost at the finished dimensions, you're asking them to take 100# of draw weight just on the tips. It's even more amplified when tillering early on, by using the long string. A long tillering string leads to whip-ended bows if you use it for too long during tillering, so combine this with thin tips and it's a recipe for disaster.
Of course, you may well already know all of this, in which case ignore it completely and hopefully it'll help somebody else out reading this at a later date!
P.s. have you read Cornwell's latest book, "1356" yet? It's incredible! Easily his best so far. I enjoyed it even more than "Azingcourt"!