Spatial room impulse responses (SRIRs) measured using spherical microphone arrays are seeing increasingly widespread use in reproducing room reverberation effects on three-dimensional surround sound systems (e.g., higher-order ambisonics) through multi-channel SRIR convolution. However, such measured impulse responses inevitably present a non-negligible noise floor, which may lead to a perceptible "infinite reverberation effect" when convolved with an input sound. Furthermore, individual sensor noise and momentary measurement artefacts may additionally corrupt the resulting impulse response. This paper presents a robust SRIR denoising procedure applicable to impulse responses with diffuse late reverberation tails, which can be modeled by a stochastic process. In such cases, the non-decaying frequency-dependent noise floor may be replaced by a synthesized incoherent tail parame-terized by the SRIR's energy decay envelope. It is shown that performing such tail re-synthesis in the spherical harmonic domain, using an independent zero-mean Gaussian noise for each component, preserves both the reverberation tail's frequency-dependent decay as well as its spatial coherence properties. The proposed process is then evaluated through its application to SRIRs measured in real-world conditions, and finally some aspects of performance and consistency verification are discussed.