I think the obvious answer is, “Call it by its normal name: friendship.”
It is a mark of our culture’s derangement that we have a difficult time conceiving of friendship and imagine there has to be some sexual component, tinge, subtext or undertone to every human relationship. Words like “homosocial” add absolutely nothing of value, but do manage, by the inevitable human tendency to respond to verbal reminders, to drag into the conversation a sexual undertone and suggestion that is not there when you simply say “friendship”. Those who have experienced deep friendship and who know how deeply false a suggestion of eros is to the sort of love that is friendship naturally rebel at this societal tendency to sexualize everything–and are then diagnosed by that society as “in denial”. Indeed, the very virulence by which they reject this silly claim is taken as “evidence” that the “denial” is deeply rooted.
Nonetheless, it is the case that one of the great gifts God has given is the reality of a true and deep friendship, not rooted in sexual attraction in the slightest–indeed, as foreign to real friendship as chocolate syrup and ice cream are to a hamburger–but in another kind of love entirely. The loss of friendship and the eroticization of everything is one of the deepest tragedies of our time. And nobody feels it more keenly than the friendless American male.