The problem with the crossover is the fact that socionics is all encompassing thought patterns, wants, needs all in one label. For example an ILE does not just equate to an ENTP, but to an ENTP 7w6 So/ (technically I suppose sexual second, but if it is there it’s certainly squished.)/ Sp. So if your enneagram and instinctual variants don’t match up you will probably find your self-caught in limbo.
The second issue is Quadra values, the circular reasoning that holds these together seems to have created a somewhat forced situation. the idea being that groups under these labels see the world in the same way; which seems to end up favouring one side over the other. For example:
Alpha Quadra; is extremely NPish; the love of abstract and complex theories, outsiders and weirdoes, aesthetic appreciation, if it’s a NP trait it would probably be considered Alpha. Also seems to be tied in with head types.
Beta Quadra is if you mixed together STP and heart triad traits, and then for the IEI, and EIE poured a SFJ façade over top of them (The whole prim proper college lit professor in love with a bad boy biker dynamic, what in MBTI people would consider the stereotypical STP and SFJ relationship.).
Gamma Quadra is probably the most diverse, they seem to be a mix of NT and TJ, and heart and gut triads. LIEs are classically NTJ, but ILIs seem to be NTJ traits mashed with NTP ones.
Delta Quadra is a mixture of strong SJ leanings with a smattering of NFP tendencies. Actually come to think of it they really are viewed as the SJs of the socionics world; they tend to get a lot of negative commentary. Admittedly they all do though Alpha and Gamma notably less so; Alphas are overgrown children, Betas are brainless social climbers, Gammas have a silver halberd stuck up their backside....... but Deltas are the stodgy scions of the Abrahamic religions, and all the tragedies that spring from it, which does seem a tad harsh.
Which I suppose is really just a long winded way of saying that you will probably find yourself testing true to enneagram and instinctual variant then to JCF.