Preparing high-quality 360-degree video for HTTP Adaptive Streaming requires encoding each sequence into multiple representations spanning different resolutions and quantization parameters (QPs). For ultra-high-resolution immersive content such as 8K 360-degree video, this process is computationally intensive due to the large number of representations and the high complexity of modern codecs. This paper investigates fast multirate encoding strategies that reduce encoding time by reusing encoder analysis information across QPs and resolutions. We evaluate two cross-resolution information-reuse pipelines that differ in how reference encodes propagate across resolutions: (i) a strict HD -> 4K -> 8K cascade with scaled analysis reuse, and (ii) a resolution-anchored scheme that initializes each resolution with its own highest-bitrate reference before guiding dependent encodes. In addition to evaluating these pipelines on standard equirectangular projection content, we also apply the same two pipelines to cubemap-projection (CMP) tiling, where each 360-degree frame is partitioned into independently encoded tiles. CMP introduces substantial parallelism, while still benefiting from the proposed multirate analysis-reuse strategies. Experimental results using the SJTU 8K 360-degree dataset show that hierarchical analysis reuse significantly accelerates HEVC encoding with minimal rate-distortion impact across both equirectangular and CMP-tiled content, yielding encoding-time reductions of roughly 33%-59% for ERP and about 51% on average for CMP, with Bjontegaard Delta Encoding Time (BDET) gains approaching -50% and wall-clock speedups of up to 4.2x.