Just installed a swept bar with a bit of rise in it ... an FSA Metropolis, 31.8mm clamp, 46º back sweep, 21º up sweep, 300gr weight.

Installed slightly aimed downward, there's very little overall rise. Installed "straight" then it'll be the full 21º rise. Installed upside down, even, it gives you a bit of drop. As compared to a flat bar with a single-digit degree of sweep, it's a nice intermediate bar. Like you, OP, on this bike I dislike the relatively flat, straight bars typical on MTB style bikes. But I really didn't want a "cruiser" style with massive sweep and rise. This one's a reasonable compromise.

Has brought my hands rearward about 50mm from the flat bar's position, and given me some control over the rise. Am considering the Ergon GC-1 grips for swept bars, but might well not need to additional off-line change they provide, as the wrists are fine right now.

Much nicer riding position, given my bike's overall geometry and stem.

Also considered the On-One Mary bar, along with the Soma Clarence 31.8mm bar.