A few choices spring to mind. There may be others. The first is to find someone who is asexual - doesn't want or mind not having sex. But, if you do and your desire wicks back up, then you might find yourself on an unhappy island.
The second choice is exactly what you seem to be considering. Be open about this aspect of your desire (where it is and where it isn't) and allow your partner to have other relationships (purely sexual or otherwise) to create the opportunity for the deep connection you seek.
I - for one - am open to this kind of relationship as long as I can continue to be poly. I often describe my relationship with one of closest friends as a platonic romance. It is more than a friendship but there is certainly no sex and never has been. I love her deeply and am perfectly happy to give up sex with her to stay connected with her in all the ways we can connect.
Being clear about that can be very useful (and successful) in my view. Don't assume, however, that it'll come without heartbreak, confusion, etc. that are natural parts of human love. That'll still happen. But, you open up the possibilty of finding something special that meets your needs.
Male, Straight, Poly
“Instead of getting better and better at avoiding, learn to accept the present moment as if you had invited it. And work with it instead of against it. And making it your ally rather than your enemy.”