Ah sorry I completely overlooked the monologue aspect, I've been going from the volcas to a mixer to get two of them running at once nicely. I meant to answer your original question and got off on a tangent.
So the Monologue is 1/4" mono, which you could go with the breakout 1 to two cable and leave the unused 1/4" out, or try this cable
I think you would be ok in either event. The problem comes from the "balanced" inputs on mixers and such not playing nicely with the headphone jacks.
3.5TRS to 1/4" TS sorry. [this one](Hosa CMP-105 1/4 inch TS to 3.5 mm TRS Mono Interconnect Cable, 5 feet https://www.amazon.com/dp/B000068O3F/ref=cm_sw_r_cp_api_nFtKybFDZQEWJ) specifically. Cheap enough to experiment with.
I've got the FM on a 3.5 TRS - 1/4" TRS now and having loss issues through the mixer.
I've tried multiple cable combinations and not getting the same sound as with headphones. I haven't been able to find anything online that gives a definitive answer as to what cables each volca needs for different applications.
Which is why I'm experimenting further with the 3.5mm TRS to split 1/4" and the 3.5TRS to 1/4" TS.
this guy's video is so far the best info I've found.
This is your cable. I bought these when I ran into the same issue with my FM and Sample:
https://www.amazon.com/gp/product/B000068O3F
Had initially purchased these but they behaved as you described so I had to buy the first ones: https://www.amazon.com/gp/product/B08233VCKK