In my experience (disclaimers are important) the sideburner stove designs require broad bottom pots, minimum of 4.5", typically 5"+, and are fast and efficient, with no simmer options. Here's some great examples, by no means exhaustive (another disclaimer). No need to mention the Caldera again.
wide diameter pots, fast and efficient:
Minibull
ThruHiker (George is a good guy and makes his designs available in the MYOG threads)
small diameter pots, simmer options:
Brasslite
FeatherFire
Mini Bull Designs
I don't have any real experience with simmering. I imagine the above options could work with larger diameter pots too. Regarding cooking with a simmer, it sounds interesting, maybe even fun, it also sounds tedious in camp. And anything that needs to operate for 20 minutes seems like an opening for issues. If you want to cook lentils or rice or pasta, I'd strongly consider dehydrated lentils and pasta (DIY or Online purchases, checkout the Food threads, specifically Susan's comments), and partialy cooked, ready rice. Freezer bag cooking is fantastic: all home prep; boil water, apply; wait 8minutes; eat; lick yer spoon; roll the leftover bag, yer done!
Also, it should obvious by now that UL involves more gear, and few, if any, do-it-all components. Plus a commitment to personal testing, nothing less is truly convincing. Expect to own a few or half-dozen stoves before you settle with any two or three favorites that handle your various needs. Have fun.
-Michael