In short, there isn't any extra way to avoid Background counts.
The only thing you can do as an awakened is avoid the BC count, become acclimated to it so it no longer effects you.
Its important to note what a BC does to an awakened.
Street Grimoire Page 32
A background count impose a negative dice pool penalty
equal to its rating for all tests linked in any way to magic (such
as spellcasting, summoning, and skill tests that use active adept
powers such as Killing Hands or Improved Sense)....
...Dual-natured creatures
or purely astral creatures take a negative dice pool penalty to all
actions equal to the background count....
...Pre-existing active foci, sustained spells, quickened/anchored
spells and rituals are reduced by the background count. If they are
reduced to 0 or less, spells fizzle, wards and rituals collapse, foci
deactivate. A foci cannot activate while under the influence of the
background count.
Which basically means that centering for an adept is the only way to avoid the dice pool hit, at the cost of your free action AND the fact you have to be initiated to take centering in the first place.
(Warriors Way does nothing to help with BC, its only advantage is less foci binding costs. )
Street Grimoire page 178
THE WARRIOR’S WAY
COST: 20 KARMA
The Warrior is the type that most mundanes associate
with the word adept. These elite combatants dedicate
their lives to forging their bodies into lethal weapons or
engines of war. Combat is their calling, and they excel
at it, accomplishing through skill and magic what others
use augmentations to accomplish.
Bonding a weapon focus costs two less Karma than
normal for those following the Warrior’s Way.
Warriors can choose from the following list of powers
for their discount: Blind Fighting, Combat Sense,
Counterstrike, Critical Strike, Improved Ability, Improved
Potential (Physical), Killing Hands, Missile Mastery, Motion
Sense, Rapid Draw.
Acclimating to a background count takes weeks to month of exposure to the BC in question, but happens naturally. Which is one of the reasons mages don't like leaving their cities of operation. They are acclimated to the BC of their area/city and are not affected by it. However, working in a entirely different city/area exposes them to that City/area background count, making their magic that much harder to use.
For example:
John-boy is a mage from Chicago where the Back ground count is 5. To John-boy, because he has grown up there, the BC of the area has no effect on his magic at all, and doesn't even notice it. One day, John-boy takes a job in Seattle where the BC is 2. Suddenly everything John-boy tries to do magically while in Seattle for the run takes a dice pool modifier of -2, and any foci or sustained spells that he had active are reduced by 2.
While in Seattle, he meets Sally Spellslinger and hits it off. Sally decides to follow John-boy back to Chicago. While in Chicago, Sally Spellslinger takes a -5 dice pool to all magic related tests, and any active foci or sustained spells are reduced by 5! Sally toughs it out and stays in Chicago for 2 months, after which she has grown acclimated to the Chicago Background count, and she no longer takes -5 DP hit to her tests. (However, if she was to move back to Seattle, she would suffer the same -2 DP that John-boy suffered when he came to Seattle. Until she was acclimated back to the Seattle background count)
Sadly, BC counts and the dice pool hit is the cost of being awakened... and while it can suck, it is not as bad as many people think it is, but it can throw a spanner in the works if you are not prepared for it.