Hey folks we're talking about a 10k budget! This isn't really about mono vs. multi, despite the OP's question: It's about whether he can get a safe ocean-ready boat capable of handing a storm or two.
I acknowledge that people have crossed oceans in rowboats, but I think if he found a decent hull
for $0-5k he'd need to spend more than $10k to get a boat (any boat) to ocean-ready condition. It would also involve a lot of sweat equity. I don't think there's any such thing as an ocean crossing
ready boat for $10k in sail away shape. Not mono, not multi. JMHO -- Yours may vary.