Is there a way to constrain a part from vertically through a hole on a conal surface?

The attached file shows what project I've been working on. All the fittings are constrained to be aligned with the holes. I know in usual cases you use a mate to make the bottom of the face of the flange not move from the lid and offset it. But since the surface is conical it creates a conflict in relationships or something. Also, I've tried to use the insert constraint on them (and I've made the holes by both embedding through and using the hole command) but it refuses to do so. Is there a way to make this insert command work with these holes? That would fix all my problems at the moment. :) Thanks in advance

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