Is there a performance difference between the different designs/locations of reflex all else being equal? To clarify, will there be a performance difference between a longbow with even, consistent reflex and a recurve where the only reflex is at the tips, and all else (length, weight, tip weight, amount of reflex, wood type etc.) is equal?
This question has been asked many times and is very difficult to answer because so much of the performance resides in the fine details. Assuming the same amount of reflex, bow length, etc. these are some of the things I have found in designing bows using software. These are by no means definitive or comprehensive, just some of the results I have seen:
1) The recurve will store more energy than the long bow.
2) An evenly reflexed limb adds a bit more stress to the wood than a recurved limb.
3) The recurve will provide a smoother draw cycle than the long bow but is significantly harder to tiller. The smoother draw is shown in the analysis, but the tillering difficulty is from practical experience.
4) The recurve usually needs more wood in the limbs towards the tips to keep the limb from twisting through the draw. This increases tip mass and reduces performance. I know you said the same limb/tip weight, but you typically just can't do that and have the recurve work.
None of this really answers your performance question, because modelling that is beyond any software and ability I have. I can calculate stresses and energy storage, but performance is really about maximizing the energy transfer into the arrow. This is why the super recurve FG bows don't perform that much better than a highly optimized more conservative design. They store a significantly higher amount of energy but they struggle to get that into the arrow efficiently. To keep the limbs tracking they need to be quite heavy all the way to the tip and this hurts the performance a great deal.
In general this is why wood bows get so close to the FG bows while using a significantly lower performing material. FG should absolutely blow wood out of the water, but it doesn't because wood is easier to extract most of the potential from while FG is not.
If you want to try adding reflex, I would suggest starting with an evenly reflexed long/flat bow design. It is easy to make a form to heat it into shape or to glue up a simple backed bow on and you can make it a basic pyramid design with nearly even limb thickness that is simpler to tiller, which is always a bonus when trying something new. I wouldn't add more than 2-3" of reflex at most on a 64"-66" bow for a 28" draw. A lot of what reflex does is increase string tension at brace and early draw weight and the extra tension at brace makes it harder to get the string on the bow. The extra difficulty in stringing goes up surprisingly fast with just a little bit of reflex.
Well, I guess that's my novel chapter for Sunday morning...
Mark