I may have already addressed this argument with my comments about the undue reductionism of Greek love terms in my other post, but in case not, I will elaborate.

I don't know how bound you are by 'anything I recognize as a word is completely separate from anything else I recognize as another word' but assuming you do recognize the reality of conceptual intergradation among words, you may at least picture how I might logically tell you the following.

The quintessence of loving eros (as opposed to alienated arousal as in rape) is a sense of fusion in the perfect mix of Other and Self that is your partner. The wetness of conventional sex with its metaphor of a return to birth and childhood and perhaps even to the primordial seas usually serves as a talisman for this melting into each other, but it isn't completely necessary. Deep spiritual union of Self and complementation of Other is the gist of it. It intergrades as a mystical experience with the supreme religious experiences of saintly mystics like St. Teresa of Avila. This is why marriage is a religious sacrament, not just an interaction. It is why religious mystics often choose celibacy - they try to reserve this union for God alone. It is what the RC church hopes to facilitate with celibacy, above and beyond freedom from worldly affairs. God does not disdain to enter into this ecstatic eros with his mystics; nor does Jesus.

As for stainless and selfless agape, the poise of caring for another as a most life-sustaining duty and objective is most easily seen in care for a sick partner or care for an economically disadvantaged partner. It is also found, though, in care for a partner who experiences the vulnerability of a biological sexual imperative -- and who chooses to express it not into a bedsheet or a tissue or a prostitute or a chance acquaintance or a socially forced union with a repellent partner of the unattractive sex, but instead in a lifelong dedication of mutuality with you, the beloved - giving the highest reality to Marvin Gaye's phrase 'sexual healing.'

An orgasm without agape is self-serving; a prayer without eros is the lowest stage of religious illumination.