Earlier studies of β-Myrcene (Myr)/ β-ketoester functional (acetoacetoxy)ethyl methacrylate (AAEMA) copolymers exhibited compositional drift, leading to ambiguity in microstructure/thermomechanical property correlations while shape memory recovery times were excessively long ~1 h. The terpene-based 1,3-diene Myr and AAEMA were copolymerized via nitroxide-mediated polymerization (NMP) with an initial Myr molar feed ratio ranging from 0.1 to 0.9. Reactivity ratios estimated by the Meyer-Lowry method were rMyr = 0.20 and rAAEMA = 0.22 with respective 95% confidence intervals of [0.13, 0.37] and [0.15, 0.23], suggesting alternating copolymerization. Bulk terpolymerization with styrene (Sty) afforded linear poly(Myr-stat-Sty-stat-AAEMA) prepolymers designed to modulate glass transition temperature Tg and stiffness. Subsequent cross-linking with isophorone diamine (IPDA) formed catalyst-free vinylogous urethane dynamic linkages. ATR-FTIR, dynamic mechanical analysis (DMA), and tensile measurements confirmed the recyclability of vitrimers through hot pressing at 110 °C, demonstrating minimal changes in rheological and mechanical properties even after four cycles. By heating the vitrimers to above their Tg (to ~45 °C), they exhibited a shape memory effect with high shape fixity and fast shape recovery (< 1 min). The vitrimers could undergo permanent shape reprogramming through reconfiguration of dynamic bonds at ~110 °C. This work shows the adaptability of Myr-based rubbers by vitrification and appropriate copolymerization for the synthesis of more sustainable elastomers with stimuli responsive properties.