Umm... you're not going to get space, speed, safety and a shallow draft in a single boat as a general rule. An Alberg 30 is one boat I can think of that two people could liveaboard, and IIRC it has about a four-foot draft.
However, it really sounds like you want a small catamaran, like a Catalac 8M. This would give you shallow draft, lots of space, fairly good turn of speed and is pretty safe. The Heavenly Twins 26, the Iroquois MkI or MkII, the Gemini are other catamarans that might fit the bill as well.
Most monohull sailboats, that have a shallow draft have to either give up storage or safety for the shallow draft. Most won't be less than four feet in a shallow draft version, and the few that are may be too small for two people or way out of your budget, like the Shannon Shoalsailor.
All four of the catamarans I've mentioned have made Atlantic crossings, but have a board up draft of less than two feet IIRC.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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