Transience of the balanced excited random walk M(3,2,1)

Prove that the balanced excited random walk M(3,2,1) is transient.

Background

The paper reviews known recurrence and transience results for the family of balanced excited random walks M(d,d_1,d_2). In the non-overlapping case d_1+d_2=d, projections establish transience when max{d_1,d_2} is at least 3, and M(4,2,2) is known to be transient. The transience of M(3,1,2) was subsequently proved, but the analogous case M(3,2,1) is identified as a remaining conjectural case.