So, I've also been looking into producing a rum product, but until two months ago I had never done a sugar or sugar-byproduct fermentation before.... I found that my first ferments were just too...clean and uninteresting, which lead me down the Arroyo/high-ester rum rabbit hole.
At first I was just adding back stillage to my ferments at approximately 25% of their volume, which also made very clean ferments. Luckily I live in the land of sugar, and I had some leftover agricole juice (no treatment, it started naturally fermenting within hours of picking it up from the mill) that I had pitched with Brett dregs. I've been keeping this culture of natural yeast, lacto and brett to reinoculate my stillage before I actually set up my ferments.
Much like fermenting sugar I've never kept stillage before, and I don't know what best practices exist to encourage the right fatty acids to form and then to keep until I am ready for the next ferment, but here's where I am in my line of inquiry for making rum ferments more interesting based on what I've read from Arroyo and Boston Apothecary. It is a very loose regimen, and I am playing with a lot of the parameters. These experiments seem to multiply:
1) Stop your ferment so there is some sugar left in your stillage (~1.010) for your Brett to eat.
2)Pitch your bug culture into your cool stillage and let sit for a week or more before you need to set up your ferments. I have not been adjusting pH at this point even though my stillage pH sits between 2.91-3.3. I am currently in the middle of a line of experiments and I will be adjusting pH at this point in the future, however I usually see activity on the surface within a day or two.
3) Add bugged stillage to your new ferments at a 25% rate and adjust pH to 5.2. I also add a "normal" yeast at this point.
This method needs serious refinement, but the results are really interesting. It's still far less funky than my goal, and it has raised more questions than it has answered (common lore is that untreated agricole juice goes sour/bad a few hours after the cane is cut, but if it's immediately fermented, how long can you keep your cane beer?). I may not be heading in the right direction, but they are all interesting unknowns.