Can I get rid of this wood fiber taste? The first thing I taste when I make coffee is a wood fiber taste. By the second sip, its gone and the coffee tastes tolerable. 

I buy a Costa Rican Arabica roast from BJ's. I buy several pounds and stick it in the freezer. I grind before brewing. Have just bought a Breville Smart Grinder Pro and a Behmor Brazen Plus drip coffee maker (gold tone paperless filter). My grind size on the Breville is 48, the high end of medium according to their guide. However, I might be inclined to call it fine as pictures I've seen on the web lead me to this conclusion. Also, grinds tend to float in the air as I grind. As to the Brazen, I brew at 204 degrees with a 1.5 minute soak cycle. I use eight cups (setting) of grinds to make six cups of coffee. I intend to experiment but I'd like to hear some expert advice also. 

So, the question is, can I avoid that wood fiber flavor or am I stuck with it?
I would suggest buying any other kind of non-flavored coffee (or borrowing some) and using your same parameters to make a pot.  That should determine whether your machine/process is imparting that taste to the beans or if it's just the coffee itself.  

Lightly roasted coffee often has tastes described as woody, grassy, or sometimes tea like.  This can vary from very noticeable at light roast levels to not at all noticeable at moderate levels.  Even if you have purchased those same beans before and were not expecting the taste, it's possible you purchased a bag less roasted than previous bags you have bought.