While folks have thrown out lots of good ideas, I think the next step for you is finding a really good fitter. I know that is not easy, but it seems a previous poster gave you a good suggestion, so before you buy a new stem or bars, I would explore that. I am sorry but no matter how well meaning we are, there is no way a bunch of folks can fit you to your bike on the internet. Sure, you can collect information on solutions that have worked for others to share with your fitter, but you need to be fit by an experienced person that can watch how your body responds to subtle tweaks.

Indeed, saddle position needs to be set for power over the pedals, not to correct a reach problem. Then stem length, stem height, bar reach, drop reach, drop shape, and lever positioning, are all paramaters that can be manipulated, and are influenced by your flexibility and personal preferences. I too MUST have my bars parallel to the ground, or the drops feel wrong, but I also like them flat on top, which you can get with the right bar and lever positioning.

I figured this all out the hard way, and then only finally as part of a new bike purchase did I complete my journey by discovering that the owner of a local shop that I had never tried before has outstanding fitting skills.

Good luck to you, and keep us posted how it works.