I have a free standing wood stove in the basement that can take 18" pieces.  I'm an opportunistic firewood collector taking whatever is dead on my lot, typically oak, ash, birch, with some white pine thrown in when it's close to the house.

I've got some wood stacked inside a pole shed that's been there 10 years and bone dry.  More recently I stacked it outside without a cover, and it has rained a lot this year.

My method has been to make a stack of outside wood about three feet from the stove, then burn inside for two weeks +/-.  After two weeks I burn the "outside" wood until it's gone, then replenish both stacks.

How much of a difference on the "outside" wood do think I'm making in that two week's time?  Is two weeks long enough to draw out the moisture any appreciable amount?

If the outside wood is seasoned and only wet from rain then it should dry out in a day or two by the stove, of course the dryer the better so...

the rain doesn't increase the moisture content on dried wood all that much
unless it's sitting in a puddle

I used to store all my wood outside uncovered and brought in just a couple days worth at a time.
never had any problems, just knock the snow off and go

I miss my wood burner

Firewood-sized wood is generally 1,000-hour or 10,000-hour sized fuel, meaning it takes between 1,000 hours and 10,000 hours to equalize with ambient temp/humidity.

1,000 hours is ~42 days.

Different species of wood have different drying times and different amounts of sap / resin.
The following considers cut to length and split to stove wood size...YMMV
OAK, dry for 2 years... very dense wood.
MAPLE, dry all summer, put under cover and burn in the fall / winter.
ASH, Can be burned green right off the stump but a couple months of dry time are recommended.
BIRCH, BEACH & POPLAR.. Smolder, stink and provide little heat. OK for spring and fall.
PINE, SPRUCE, FIR & HEMLOCK... high resin content, will build creosote in the chimney, Great for kindling if dry.
APPLE, BEACH, ELM.. wicked hot burning, miserable to split, gnarley stuff!!!
How do I know these things??
Sold firewood for years, cut, split & delivered thousands of cords. Burned wood all my life..
You want real hot real fast??? Alders and apple limbs (pecker pole size) will melt a fucking stove...
Stove pipe so hot ya could prolly read news print thru it...
Trust me here... we've had some hot suppers with a wood stoves / furnaces / boilers..
Got boiler?? Learn the "steam table" Seriously look it up!! That shit will mess up your life permanently!
Be careful, be safe and think things through!!

Just what is this 'BEACH" wood?  We never learned about that in dendro.

And how can "BEACH" smolder, stink, and provide little heat but also be wicked hot burning?

I'll take with a large grain of salt anyone who's sold firewood for years but still doesn't know BEACH is really beech.

Lol, I was going to point out the same thing.

I disagree w/ many of his assertions on burning characteristics etc. Sometimes it's tree dependent. IE, usually soft maple is a good burner... I've got some nasty twisted silver maple that came from a 52" DBH tree that just smolders. It's solid, hard, and twisted; I dread getting a piece in the stove on startup bc it just won't light.

As far asthe OP's drying, as long as its not Oak your 2 week process sounds about right. Keep doing it if you have enough dry wood to keep going with it. That being said, just get a wood moisture meter, Harbor Freight has them for ~$8 IIRC

What?  Beech has some the highest BTU outputs of all of the Eastern Hardwoods.  Up there with White Oak.

I burn 6-8 cords a year.  I burn everything except Willow.  Poplar, Sassafras, Red Oak, and Black Cherry.  Dry, it all works.  I really like Red Maple and Poplar, it burns with a nice bright flame and is clean.

I highly recommend the book Norwegian Wood, by Lars Mytting if you want a good read.

I'm more curious what "pecker pole" size is.

I'll let the "beach" slide, unless he's referring to driftwood on the beach.