Everyone is different. If it seems to work for you, it seems to work for you.
Of course, a small change and it might all work much better. (Please pardon the bad photoshop---I am go0ing to be late for work because I messed with this too long already.)
I didn't get it quite right but if you look how you have it set up, the flats slope down at about 20 degrees .... which means if you rest your hands there, they are always sliding forward toward the hoods. This means you have to use extra strength the stay on that part of the bars, which defeats the point of a good set-up, which should keep your in a few optimized positions effortlessly. (IMO)
The modified pic is a little off---the bars are supposed to he horizontal, but I rotated them two degrees too far (you just can't hire good help anymore---or, you get what you pay for.) What I am trying to show is that if the flats are actually flat, you can rest anywhere on the bar from the outside of the curves all the way to full-on grabbing the hoods, and always have a level platform for support underneath, so you don't have to actually Grip with your hands to stay in place---you can wrest on the bar and just wrap your fingers around the bar or brifter in a relaxed fashion until you need to make control input motions.
Most people seem to favor this set-up. A lot of older (to you, ancient) competitive riders used that steep downslope to the brake hoods because they rode either the hoods or the drops, and not so much on the bar .... different way of approaching things---but look at the modern peloton and see how they are set up. Doesn't mean it will work for you, but pretty much all of them have horizontal flats (and the brifters angled in a bit toward the centerline, which is a separate issue.)
As for reaching the drops, that is more about the shape of your bars versus the shape of your body. You want (again, IMO) the drops to be easily and comfortable reachable---back in the day, people used Huge bars with eight inches between tops and drops. Nowadays, most bars are about 70-150 reach and maybe 125-150 drop---more of a natural downward and forward swing of the body to fall onto the drops. If your bars are shaped to fit your body, you should be able to ride in the drops without much stress or reaching, and without any more pressure on your hands than when riding on the hoods .... but that is both bar shape and bar position. Needs tweaking as a rule to get it perfectly suited to you.
When I ride the drops it is my swollen belly, not the pressure or distance to the drops that makes me sit up sooner---I like to breathe, and stuff which stops me from breathing, I don't do for too long. Still, on every bike I have my set-up adjusted so I can ride the tops, the flats, the hoods, or the drops without hurting my hands or wrists or locking my elbows or doing any other damaging thing. I like to rest on the bars and hold them, not grip them.
(Sorry ... flats are supposed to be flat but I left them tilted down a bit .... oh well.)