If you're going overnight, personally I would use the fridge. Definitely think the oven on proof cycle with lead to over-rising and then a poor final rise (as the yeast will have eaten everything they can too early in the process).

I haven't looked Lahey's recipe yet in detail, but I would be averse to using the proofing cycle for more than 6-7 hours or so of the total process (bulk rise, loaf proofing, etc., combined). I'll have to go read though his recipe now...

ETA: Read through Lahey's recipe, and I still think the standard proof cycle might be a bit warm for overnight. A 12-18 hour bulk fermentation like he suggests would be at room temperature of 68-72 IMHO, and at warmer temps would risk the yeast basically running out of food too quickly, and the final dough falling a bit. You might be okay; always worth trying. I left my dough to autolyse in the oven on the proof setting the other night, and it oxidized a bit. Still mostly worked ok, but had yeast been there, it would have been messy (I added the yeast the next morning, then let it rise for about 3 hours and proof for 1-2 more after I'd shaped it roughly; it came out pretty well). But most overnight rises I've used have indeed been either in the fridge or with ice water to start.