I've made the swag with a glass globe; however, when I hang it the weight of the globe puts too much pull on the wire. The globe slides slowly to the floor on the tense wire leaving the chain behind.

You have something seriously screwed up.
The chain is what is supposed to support the fixture, not the wire.

There should be a chain loop ring on the lamp globe and the ceiling box cover. The chain holds the light and the wire is woven through the chain. You are missing something.

The fixture needs a direct connection with the chain, and if going across a ceiling with hooks, only the chain should be on the hook. I usually thread through every other link.
Once hung, adjust the wire through the chain so the loops hang straight with no tension on the wire.