There are always new studies. I’ve not conducted any, but my review is that most studies are inconclusive for various reasons. Results tend to range from statistically insignificant, to favorable maximal power output for oval rings by up to approximately 6%. I’ve yet to see a claim that non-round rings are detrimental to performance.
From a mathematical perspective, it is simply not possible for circular rings to optimally load leg muscles under maximal power, if by optimal we mean that the required power for each muscle group is proportional to their relative capacities.
From a practical perspective, the deviation from circular that may be required to achieve various “optimal†load demands as a function of crank angle may exceed that which allows for shifting without issues under racing demands.
Under sub-maximal efforts, cyclists provide their own “weighting function†by simply employing each muscle group in proportion to their desires and abilities. One can observe this in any pedaling power output scan, which tends to show a “peanut†shaped distribution with crank revolution. I believe this self-selected muscular loading is what clouds many studies.
Intuitively, consider measuring the maximum torque you can apply with cranks at 12 and 6 o’clock at a stand-still, with the rear wheel locked in place. Then try the same with pedals at 9 and 3 o’clock. This represents the maximum torque one can possibly provide to the pedals at each position, since allowing any rotation of the crank reduces the resistance. Approaching extremely high cadences, pedaling torque is significantly reduced (see studies on BMX racers). At low-momentum efforts, one is less able to self-select muscle loading, as there will be minimum torque required for a given crank angle at X rpm and Y power, which is likely to hurt more at the top of the stroke than the downstroke, hence people “pedaling squares†up steep slopes.
I’ve played around with crank angle on my oval rings and definitely have a preferred angle of +5 degrees. Under maximal efforts I also prefer the pedaling torque distribution of an oval 53 chainring which peaks at equivalent to 56 but is only 50 near the top of the stroke. When cruising at something like 70% FTP or below, I don’t think the difference is noticeable.
I have not tried QXL or Ossymetric rings, but I’d consider them for time trials, and probably not for conditions where I’d want fast reliable shifting.