We present an x-ray regenerative amplifier free-electron laser design capable of producing fully coherent hard x-ray pulses across a broad tuning range at a high steady state repetition rate. The scheme leverages a strong undulator taper and an apertured diamond output-coupling cavity crystal to produce both high peak and average spectral brightness radiation that is 2 to 3 orders of magnitude greater than conventional single-pass self-amplified spontaneous emission free-electron laser amplifiers. Refractive guiding in the postsaturation regime is found to play a key role in passively controlling the stored cavity power. The scheme is explored both analytically and numerically in the context of the Linac Coherent Light Source II High Energy upgrade.