You can run fully functional underpowered anything for under $1K. I don't think the point is to run an inferior deck, though. Not saying your list is bad, but no way can you convince me that lotus petal is just better than black lotus. You can make anything "work" with budget replacement cards, but I think the OP wants a fully functional and OPTIMAL explosive list. While black lotus probably is just better in every deck and puts everything out of budget range, decks without lotus and on-color moxen can really only be justified in a deck with null rod effects imho. Eldrazi fits that bill in the right build.
The reality is, an oathstill deck wants an oath asap. Extra fast mana isn't all that important.
Within the listed budget, there aren't many options. Just flatly dismissing an unpowered list, you have to understand exactly how crucial or not power is to that list. I regularly go toe to toe with proxied fully powered vintage decks with a similar build.