Dummy plugs for headless GPU rigs

I've read about people claiming they needed to plug a monitor (or dummy plug) into one GPU card or else they couldn't use the card.  I had never encountered any problems with either fglrx or AMDGPU-Pro drivers until recently.  I moved a 4GB R9 380 card from an Ubuntu 14.04/fglrx rig to a Ubuntu 16.04/AMDGPU-Pro rig.  The remaining cards are 2GB R7 370 cards, and I started getting memory allocation errors for the primary card.  After checking with "ethminer --list-devices", I noticed the first card had about half the maximum memory allocation limit of the others:
Genoil's ethminer 0.9.41-genoil-1.2.0nr
=====================================================================
Forked from github.com/ethereum/cpp-ethereum
CUDA kernel ported from Tim Hughes' OpenCL kernel
With contributions from nicehash, nerdralph, RoBiK and sp_

Please consider a donation to:
ETH: 0xeb9310b185455f863f526dab3d245809f6854b4d

[OPENCL]:
Listing OpenCL devices.
FORMAT: [deviceID] deviceName
[0] Pitcairn
        CL_DEVICE_TYPE: GPU
        CL_DEVICE_GLOBAL_MEM_SIZE: 1920991232
        CL_DEVICE_MAX_MEM_ALLOC_SIZE: 970981376
        CL_DEVICE_MAX_WORK_GROUP_SIZE: 256
[1] Pitcairn
        CL_DEVICE_TYPE: GPU
        CL_DEVICE_GLOBAL_MEM_SIZE: 2095054848
        CL_DEVICE_MAX_MEM_ALLOC_SIZE: 1868562432
        CL_DEVICE_MAX_WORK_GROUP_SIZE: 256

I have an old VGA LCD monitor that I connected using a HDMI-VGA adapter.  After connecting the monitor, nearly the full amount became available:
Genoil's ethminer 0.9.41-genoil-1.2.0nr
=====================================================================
Forked from github.com/ethereum/cpp-ethereum
CUDA kernel ported from Tim Hughes' OpenCL kernel
With contributions from nicehash, nerdralph, RoBiK and sp_

Please consider a donation to:
ETH: 0xeb9310b185455f863f526dab3d245809f6854b4d

[OPENCL]:
Listing OpenCL devices.
FORMAT: [deviceID] deviceName
[0] Pitcairn
        CL_DEVICE_TYPE: GPU
        CL_DEVICE_GLOBAL_MEM_SIZE: 1969225728
        CL_DEVICE_MAX_MEM_ALLOC_SIZE: 1750073344
        CL_DEVICE_MAX_WORK_GROUP_SIZE: 256
[1] Pitcairn
        CL_DEVICE_TYPE: GPU
        CL_DEVICE_GLOBAL_MEM_SIZE: 1968177152
        CL_DEVICE_MAX_MEM_ALLOC_SIZE: 1750073344
        CL_DEVICE_MAX_WORK_GROUP_SIZE: 256

I also found the monitor doesn't have to be plugged in, just the HDMI-VGA adapter.  While there might be a way to configure fglrx so that the full memory is available without the adapter, I'm more interested in learning more about AMDGPU-Pro.