Lord Gryn's schemes had been a tightly interlocking game of chess. His original script had been... when the time was right, he would be forced to temporarily pardon Stannis in the name of preserving peace in the Seven Kingdoms, allowing him to redeem himself through meritorious service.
Then.
The ruthless Stannis, known throughout the Seven Kingdoms, would exploit King Gryn's mercy and the laws of the Seven Kingdoms to thoroughly purge the realm—especially the Westerlands.
Gryn would then rightfully strengthen the power of the Targaryen-Crabb royal house.
Then, merciful Gryn would once again, for the peace of the Seven Kingdoms, have Stannis Take the Black and exile him to the Wall of the End.
Finally, news of the White Walker invasion would spread throughout the Seven Kingdoms. Wise King Gryn would override all objections and appoint Stannis commander-in-chief of the "Burning Legion," ordering him to lead the newly "created" criminals and red priests beyond the Wall as the vanguard of the living.
In addition—Ser Jaime would be appointed first deputy commander of the "Stannis" Legion.
One of the key reasons for choosing to take the initiative and attack... was the need to quickly test the effectiveness of a large-scale battle between a human legion armed with Wildfire and Dragonglass weapons and the White Walkers.
That way, the armies of the Seven Kingdoms within the Wall would have more time to adjust their traditional tactics and strengthen their training accordingly.
In this war concerning the survival of the realm of the living, Gryn's sole objective was to utterly defeat the White Walkers' army of Wights.
However...
A plan was ultimately only a plan; it could never overcome the uncertainties of the human heart. Even His Majesty Gryn had not expected Stannis to choose to assassinate Duke Ned, though it was not