Acoustoelectric imaging (AEI) maps physiological current sources in tissue with spatiotemporal resolution set by the ultrasound pulse and beam. Conventional focused-beam scanning limits full 3D reconstruction due to the tradeoff between volume rate and field of view (FOV). Here, we present Hadamard synthetic beamforming (HSB) for full 3D AEI, along with strategies to reduce the transmit sequence for high-volume-rate imaging. This reduced-sequence HSB approach groups elements along one array dimension while applying transmit-focusing delays to preserve image quality and point spread function. Although this reduces subaperture elements and FOV in the encoded dimension, we quantify this limitation and show it is acceptable for biocurrent imaging. We validate the method using a 16 × 16 array at 0.6 MHz to image 200 Hz dipole sources in a tissue-mimicking phantom and through a 6 mm human skull at f/# = ~1. Reducing the sequence to 16 × 4 increases volume rate fourfold while maintaining a moderate-to-good elevation FOV of ±5.8°. At 10 cm depth with a 15 kHz pulse repetition frequency and 256 transmissions, volume rate increases from 58.6 to 234 Hz, sufficient to resolve gamma-band (~100 Hz) neural activity. Full HSB provides a theoretical SNR gain of 8.3 dB over focused-beam scanning after pressure equalization, while reduced-sequence HSB retains a 2.3 dB gain. Skull experiments confirm reduced-sequence HSB reconstructs 3D current fields comparable to full HSB. Most importantly, reduced-sequence HSB recovers all three current-density components at physiologically relevant volume rates over a practical imaging volume, impractical with conventional focused-beam scanning.