Well... resident Viking buff to the rescue, I guess...
The Vikings were fatalists... they firmly believed that fate was undeniable, in the grand scheme: not to say there was no free will... it was the broad strokes like when you were going to die that couldn't be changed... so if you were slated to die on the 5th of March next year, you were going to die on the 5th of March whether you spent every day until then jumping out of airplanes without a parachute, or lounging on your couch eating cheetos...
For them, it was an aid to courage- you may as well go into battle, and go for broke being a complete and total badass, cause if you weren't slated to die, nothing could kill you... and if you were, you may as well at least be remembered as a total badass, right?
I'd say that's the big litmus test... because the Einherjar are slated to do the exact same thing again- the battle Odin's saving them up for is a LOSING one... and he knows it, and so do they... but they're on board anyway. I think the Valkyries are interested in any warrior who has the exact kind of courage to dedicate themselves to a losing battle- whatever the reason (be it personal glory or doing what's right). Those who died in the process of pursuing (personal glory or doing what's right or whatever) have already proven themselves dedicated... and those who do so in battle are already proven warriors.
If anything, the losing side in a given battle's likely to have more candidates.... especially in a massacre like Gallipoli or Custer's Last Stand, etc.
Survivors may still stand a chance- after all, it just wasn't their time, and that's no mark against them... but they ARE less likely to be noticed by a valkyrie if they die in a hospital bed... maybe if you made a name for yourself- they might be on the lookout for Medal of Honor winners being hospitalized.
And Odin probably has way way more of them than anyone realizes.