It's about getting 4th now, that's all we have left to play for. LVG looks dead and all but buried. The idea of him managing to turn things around at this point seems far fetched. Sure, we could limp (or sleepwalk) into 4th somehow, anything's possible. But, again, it looks unlikely. Which means that not pulling the trigger now has Moyes written all over it: Wait until it's mathematically impossible and lose any chance, no matter how slim, of avoiding a total write-off.
In that scenario it's not a question of hiring an ideal replacement, but rather taking a punt on Who Ever as caretaker. LVG is only preferable to Who Ever if there's still some genuine fight left in him. I have my doubts about that, though.
Of course, the bigger picture is the true X factor here. Woody may have his reasons for wanting LVG to stick around beyond some forlorn hope of him turning it around. But regardless of what the long term plan is, surely securing 4th has to be a huge priority. Unless we've already reached an agreement with LVG's successor (someone who will take over regardless of whether we're in the CL next season or not). And that seems highly improbable. Well, if that someone is anyone but Giggs, that is.