We report the design and implementation of a high-performance superconducting quantum-interference proximity transistor based on aluminum-copper technology. With the adoption of a thin and short copper nanowire, we demonstrate full phase-driven modulation of the proximity-induced minigap in the normal-metal density of states. Under optimal bias, we record unprecedentedly high flux-to-voltage (up to 3 mV/Φ0) and flux-to-current (exceeding 100 nA/Φ0) transfer function values at subkelvin temperatures, where Φ0 is the flux quantum. The best magnetic-flux resolution (as low as 500nΦ0/Hz at 240 mK being limited by the room-temperature preamplification stage) is reached under fixed current bias. These figures of merit combined with ultralow power dissipation and micrometer-size dimensions make this mesoscopic interferometer attractive for low-temperature applications such as the investigation of the magnetization of small spin populations.