Blind modulation recognition (BMR) is a pivotal signal processing technology for cognitive receivers to reduce signaling overhead and improve transmission efficiency. Although BMR techniques have been extensively explored for single-carrier systems, only a few research have been published for OSTBC-OFDM systems. More troubling is that high-order modulation types will make the BMR harder because the constellation points are overcrowded. To remedy these flaws, we propose a two-stage high-order BMR approach that leverages low-complexity cumulants and projected accumulated constellation vector (P-ACV) to recognize high-order modulation types (e.g., 2048QAM). Firstly, zero-forcing blind equalization is employed to recover the damaged signal and enhance its feature representation. Next, the first-stage recognition module leverages the fourth-order cumulants to classify 13 modulation types into three groups, including PSK&PAM, square-shaped QAM and cross-shaped QAM groups. Finally, the second-stage recognition module distinguishes the inter-class signal in each group by P-ACV features. The temporal convolution network is built to tap the potentialities of P-ACV and speed up online inference. Numerical results demonstrate that our two-stage algorithm obtains a recognition accuracy of 97.37% when signal-to-noise-ratio (SNR) ≥ 12 dB and performs six times faster than the suboptimal method. Notably, it does not require prior knowledge, such as channel state information (CSI) and SNR conditions.