imgaussfilt3 on the GPU with very large data

I've got a large number of 3D data sets of approximately 1300x1300x2160 uint16 numbers that I wish to apply a spatial Gauss filter to, using sigma = 2 (a 9x9x9 kernel). My first implementation that conserves RAM by splitting the data into blocks is structured as follows:

for k = 1:blocks
    % Some code that generates correct indices here

    prefilterblock = data(:,:,indices);
    GaussBlock = imgaussfilt3(prefilterblock, sigma, 'FilterDomain', 'spatial');
    FiltStack(:,:,indices) = GaussBlock;
end

This implementation spends about 2 minutes performing the calculations for one block. Now, I have a gut feeling that this could be sped up a good deal with GPU computing, but the data size means that I can't just call gpuArray(prefilterblock), since this is too much for the GPU memory. Furthermore, since I want to filter in 3D I can't find good examples even after a lot of googling and searching here.

.

So in the end, my question becomes how do I split up my data so that the filtering can run on the GPU?

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The device info, in case it helps, is as follows:

                        Name: 'GeForce GTX 960'
                       Index: 1
           ComputeCapability: '5.2'
              SupportsDouble: 1
               DriverVersion: 9
              ToolkitVersion: 8
          MaxThreadsPerBlock: 1024
            MaxShmemPerBlock: 49152
          MaxThreadBlockSize: [1024 1024 64]
                 MaxGridSize: [2.1475e+09 65535 65535]
                   SIMDWidth: 32
                 TotalMemory: 4.2950e+09
             AvailableMemory: 3.5071e+09
         MultiprocessorCount: 8
                ClockRateKHz: 1253000
                 ComputeMode: 'Default'
        GPUOverlapsTransfers: 1
      KernelExecutionTimeout: 1
            CanMapHostMemory: 1
             DeviceSupported: 1
              DeviceSelected: 1