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The new 8.4 m LBT adaptive secondary AO system, with its novel pyramid wavefront sensor, was used to produce very high Strehl (≿75% at 2.16 µm) near-infrared narrowband (Brγ: 2.16 µm and [Fe II]: 1.64µm) images of 47 young (~1 Myr) Orion Trapezium θ¹ Ori cluster members. The inner ~41 x 53" of the cluster was imaged at spatial resolutions of ~0".050 (at 1.64 µm). A combination of high spatial resolution and high S/N yielded relative binary positions to ~0.5 mas accuracies. Including previous speckle data, we analyze a 15 year baseline of high-resolution observations of this cluster. We are now sensitive to relative proper motions of just ~0.3 mas yr-1 (0.6 km s-1 at 450 pc); this is a ~7x improvement in orbital velocity accuracy compared to previous efforts. We now detect clear orbital motions in the θ¹ Ori B2B3 system of 4.9 ± 0.3 km s-1 and 7.2 ± 0.8 km s-1 in the θ¹ Ori A1A2 system (with correlations of P.A. versus time at >99% confidence). All five members of the θ¹ Ori B system appear likely a gravitationally bound "mini-cluster." The very lowest mass member of the θ¹ Ori B system (B4; mass ~0.2 M⊙) has, for the first time, a clearly detected motion (at 4.3 ± 2.0 km s-1; correlation = 99.7%) w.r.t. B1. However, B4 is most likely in a long-term unstable (non-hierarchical) orbit and may "soon" be ejected from this "mini-cluster." This "ejection" process could play a major role in the formation of low-mass stars and brown dwarfs. [ABSTRACT FROM AUTHOR]