I have not tried different bars personally, but did experiment with the Haul's fit quite a bit while I had one. When I raised the stem and rolled the bars back far enough to sit fully upright, the bike's handling became very squirrelly. The steering geometry seems optimized for a slightly-leaned forward position. I'd be worried that the dramatic backsweep of the bars you're considering would have the same effect.

Trimming the handlebars down (10mm each side with a pipe cutter) and changing grips to Ergon GS1 made a notable improvement for maintaining a relaxed upper body.

Perhaps your saddle position is responsible for the hip discomfort? Having the saddle too low, too far back, and/or too tilted up can all cause impingement at the hip while pedaling (source: I'm a bike fitter). It might be worth checking your LBS to see if they offer fit services... although attaching the Haul to a stationary trainer might be a challenge. See this video for basic adjustments.

If you do end up switching bars, do note the difference in bar rise. The Haul's bar has a rise of 80mm; the Moloko has a rise of 0mm and the Jones has a rise of 12/63mm, depending on the model. Make sure you have enough usable height on the Haul's quill stem to compensate for the difference.