We apply for the first time orbit-averaged Monte Carlo star cluster simulations to study tidal tail and stellar stream formation from globular clusters (GCs), assuming a circular orbit in a time-independent spherical Galactic potential. Treating energetically unbound bodies—potential escapers (PEs)—as collisionless enables this fast but spherically symmetric method to capture asymmetric extratidal phenomena with exquisite detail. Reproducing stream features such as epicyclic overdensities, we show how returning tidal tails can form after the stream fully circumnavigates the Galaxy, enhancing the stream's velocity dispersion by several kilometers per second in our ideal case. While a truly clumpy, asymmetric, and evolving Galactic potential would greatly diffuse such tails, they warrant scrutiny as potentially excellent constraints on the Galaxy’s history and substructure. Reexamining the escape timescale Δt of PEs, we find new behavior related to chaotic scattering in the three-body problem; the Δt distribution features sharp plateaus corresponding to distinct locally smooth patches of the chaotic saddle separating the phase-space basins of escape. We study for the first time Δt in an evolving cluster, finding that Δt∼(EJ−0.1,EJ−0.4) for PEs with (low, high) Jacobi energy E J, flatter than for a static cluster ( EJ−2 ). Accounting for cluster mass loss and internal evolution lowers the median Δt from ∼10 Gyr to ≲100 Myr. We finally outline potential improvements to escape in the Monte Carlo method intended to enable the first large grids of tidal tail/stellar stream models from full GC simulations and detailed comparison to stream observations.