Why it can't be streamed from disk layer by layer, a sliding window of it, computed, temporary results held, offloaded it back and load the next window. Repeat till whole inference is done.
Also, if these are so much repetitive calculations in nature that you need CUDA cores to compute then why the inference can't be streamed and spread across a cluster of machines each having multiple commodity GPUs where one central "conductor/orchestrator" machines collects all the results from all the cluster participants?