Here's another idea. I'm not 100% sure it will work BUT I think it should work and it has a few advantages.
Required modules: i) Mutable Branches (or a similar Bernouli gate) ii) any mult iii) 2 lanes of envelope generation iv) a duo (or greater) VCA.
Setup: i) take your main trigger and mult it to get 2x of the same ii) take your desired audio and mult it to get 2x of the same iii) send your audio to VCAch1, and trigger to ENVch1 then VCAch1 to get the basic, non-accented output with your desired base envelope iv) send the mult trigger to Branches, dial in your desired random weighting (e.g. likelihood of occurrence), send the Branches output to ENVch2 then VCAch2, and the mult audio to VCAch2, that is your "random accent" lane v) dial in the VCA settings for ch1&2 to get your desired balance of accented vs non-accented sound vi) tap the combined audio outputs of ch1&2 to your downstream devices.
Here are the advantages of this type of setup:
a) Branches is a useful module, and not crazy expensive. Plus you probably have enough mults / VCAs already to pull this off, or else it wouldn't hurt you to have a bit more mult and VCA capacity.
b) importantly, this WILL let you dial in to taste the random weighting. Branches is a "coin toss" type module BUT you will be able to control the probability from 0-50% probability by using only one Branches output and setting the weighting control to taste
c) also importantly this gives you direct and full control over the relative levels of your accent vs non-accented sound, and full control over the envelopes of the base vs accented portions. Hence you could modulate any of those envelope parameters for further change and sonic interest
d) hypothetically you could chain this type of setup as much as you want (which would require more channels of Bernouli gates, mults and VCA) so that you have an unaccented lane and 2 (or more) completely different accent lanes running. Practically that would give you some (quantized) gradations of least to most accented notes.
e) this setup could be combined with other techniques (such as those above) to give you as much or as little complexity as you'd like.
Also worth considering instead of Branches (or in addition to it) would be any type of "neuron" or counter module (like EMW Pulse Counter). For example set up 1 counter to fire a trigger on every 3rd trigger input and a 2nd counter to fire a trigger on every 5th output. Then route those triggers similarly to Branches above. That would let you do "Euclidean" accents. A neuron module is generally like a counter but less regular (though it depends on the specific module).
In case you do want to run a few different lanes of accent control signal, THOSE could be routed through something like BossBow2 or Verbos Sequence Selector, hence you would be switching or sequencing different lanes of accents.
And lastly, a totally different option, you could just look for a module with "degree of random" as a built in option, such as Winter Eloquencer.
Interesting question. Hope this helps!