I have a slightly different take on the drying process.
(This is for Topps-era cards, so may not be pertinent to a 1915 CJ.)
After I soak something, I'll sandwich it in a folded paper towel, weigh it down a bit on an extremely flat surface and wait a short amount of time. This basically soaks up all of that 'extra' water right from the get-go.
Then
(with that paper towel now sopping wet) I'll replace it with a dry one and weigh it the f*ck down in a
permanent position and leave it for days -
without replacing the paper towel again - until it's dry
(and flat).
I prefer this
one and done (even though it's actually a quick two 
) scenario, because the process of removing any wet, pliable card and trying to resituate it inside of a different
(dry) paper towel without messing things up opens the door to human error.
In my book,
the less interaction with a wet card the better.
ETA: it obviously works better if the sun shines relentlessly (like out here in CA) or if it's summertime and/or always hot enough.