Lucas, If you want to mess around with this a bit more simply as a way to get a good mental handle on how all this stuff works, here is what I'd recommend-
Based on my analysis here of what your addition of the cardioid is doing, try adding some forward facing carioid to the crossed fig-8's as before, except try using an angle wider than 90 degrees between the 8's. The addition of the forward-facing cardioid essentially narrows the virtual angle, so using more angle on the 8's to start with will help retain ambient stereo width while still getting the advantage the forward-facing sensitivity bias and center focus provided by the cardioid. It should let you use more cardioid if desired, before things get overly narrow sounding. How much wider is going to be subjective, it's assessing the general trend in that direction which should be most informative.
All of this is illustrative of the many balancing acts between center-focus/solidity and ambient-width/stereo-openness. The same balancing act is "baked in" to standard stereo microphone configuration pattern/spacing/angle combinations (which to a limited extent we can tweak afterwards using Mid/Side readjustments). With these ambisonic recordings you gain more control over finding the most appropriate balance point by ear. The additional step of introducing a 3rd virtual microphone facing forward can potentially take that to another level.. which I don't think is happening here exactly yet unless you are applying different processing to the 3rd channel in comparison to the other two, such as EQ'ing it differently. Rather, I think the addition of the forward facing cardioid (or omni or whatever) can be fully explained in terms of Mid/Side and the resulting change of virtual patterns.
Ambisonics is essentially advanced Mid/Side. The addition of a forward facing cardioid (or omni as EmRR mentioned for close studio work) coincident with the Blumlein pair is really no different than changing the virtual pattern/angle. Assuming the level of both are identical, mixing an omni with the 8's turns the Blumlein pair into a virtual pair of 90 degree X/Y cardioids. If somewhat less omni is used, that becomes equivalent to a pair of supers or hypers with the same 90 degree inclusive angle.
Mixing in forward-facing cardioid instead of an omni does essentially the same, except it also narrows the virtual angle somewhat, due to the presence of the forward facing bi-directional component of the cardioid in addition to its omni component.
The suggestion of making the angle between crossed 8's wider before adding the forward-facing cardioid, serves to at least retain the 90 degree angle between the resulting super/hyper-ish virtual pair, if not increase it somewhat. The only real difference between doing this and dialing in a wider angled pair of super/hypers to begin with is the process one goes through in arriving at the end result. Don't disregard the difference in process even if you can end up achieving the same end result either way. Different working processes definitely affect our preference as we work toward and settle upon what sounds best.
What would leverage this to the next level and move it beyond an alternate way of making the same Ambisonic Mid/Side readjustment would be EQing the forward-facing cardioid differently from the fig-8 pair prior to mixing them. Say you EQ the cardioid to achieve best clarity and presence of the direct sound from the PA and stage, while EQing the crossed 8 pair for best ambient correctness. In addition, to get things correct in an overall global EQ sense, you'd can compensate for whatever specific EQ works best on the cardioid in your EQing setting for the 8s. As an example, if you start from an overall well-balanced point of reference with regards to frequency, and then boost midrange/treble in the cardioid for improved clarity and articulation of the sound from the stage and PA, you might want to boost the bass of the 8's even if they didn't need that on their own, in order to compensate "globally" for a better frequency-balance of the overall combination of the forward-direct and diffuse-ambient portions.
That's still essentially making Mid/Side type manipulations, but more advanced ones which equalize the sound arriving from the foreword quadrant differently than than arriving from all other directions. One of the cool things about single-point in space Ambisonics is that it is all level/polarity based. That means we can potentially split things up into as many virtual microphones as we want and recombine them without phase interaction problems. One just has to be careful that the processing done to each part does not introduce significant phase differences, so this sort of thing is probably a good place for linear-phase EQ's. Of course coincidence and lack of time-difference is also ambisonic's biggest constraint, and why spaced arrays which do introduce phase differences become advantageous.
Brief ambisonic aside- Excepting the EQ part, all this is getting close to the first-order Ambisonic control oddity of the "zoom" function, but not quite. I don't understand the zoom function well, but in my limited understanding, it essentially modifies the W component by shifting it from omni towards a more forward-directional pattern prior to doing the Ambisonic matrixing that derives the virtual mic-patterns. Don't sweat it if you don't follow that. It's pretty much above my head too, and I'm likely grossly oversimplifying it. It's a fun control to mess around with within a rather limited range though.