This.

Everybody is proportioned differently. Every frame is shaped differently. Saddle setback, head- and seat-bue angle, and stem length affect fit as well.

There is a lot more to it---if you don't have sufficient core strength or sufficient flexibility to maintain the proper alignments (comfortable while allowing power output) over the length of a ride, you will start to "cheat," rolling your hips back or putting more weight on your hands, which can overstress certain areas. Possibly you roll your back because you roll your hips back to open the hip-angle for more comfort and power---possibly your cockpit is too short (stem to saddle) so when your arms and hands are set right, you cannot extend your back enough. Can't tell from here.

Also, when you mention "if my seatpost is any higher I wouldn't be able to touch the ground without leaning the bike to one side significantly" we cannot tell if you mean standing flat-footed while in the saddle or touching a toe-tip, or out of the saddle straddling the frame. Most riders can get the toes to couch while in the saddle while staying upright---but that isn't really an important measurement. if your leg is properly extended (but not over-extended) while pedaling, the saddle height is right, and the rest is what it is. We don't set up our bikes to work well standing.

For-and-aft saddle position should be determined by the crank location---most people recommend starting with KOPS (Knee over pedal spindle) and making minor adjustments from there. Because you are putting so much force through your knees, you don't want to mess with this set-up once you get it right. Change everything else, but don't risk your knees.

I am about the same height you are and I ride (comfortably) a very small frame and a very large frame. I have been shopping for a new frame and trying to weigh which would work better between 54 and 56--54 is what I want, but the short head tube on that specific frame would drop the bars too far for my fat belly and aging back. The 56 might be a little too long, so I would compensate by using a very short stem. I am not built for biking, I guess. very long limbs, very short torso, fat belly, stiff joints.)

There are other people exactly the same height who ride 58 with a long stem and find it tremendously comfortable--or a 58 with a 70-mm stem and that works. No single right answer for all.

I would assume, coming from a state of ignorance, that if your back is forced into a curve, your cockpit is too short. Possible a longer stem could fix that---but possibly flipping your stem would drop the bars, creating a bit more length ... but possibly that would put the bars too low.

Possibly after a while you will have to blow $100 for a serious fitting. But I think you might be better off playing with what you've got a little, and reading up on bike fit. Maybe try some core-strengthening exercise. Possibly pay attention to keeping your back straighter and see if this puts your weight too far forward.

Whatever yuo do, let your body tell you what works, not the numbers, or comparison with others. By the way ... there are some interesting resources online: Bike Fit Calculator | Find Your Bike Size | Competitive Cyclist)

In bold because it is the only part of the post worth reading.