I'll come back later with more questions to help you better fill out this primer, but why not
Ornithopter instead of one of the artifacts?
Ornithopter would also give you a flying blocker that could help keep you alive against a flyer while you get your combo together.
Welding Jar seems like it would be a good include since it could help protect your 0 cost artifacts while also being a 0 cost artifact.
Battered Golem is another piece I've seen in this combo, why not it?
I get that keeping the price under $10 is important to you, but they're all around 30 cents or so each and could fall into that budget.