Force a resolution on a Mac Mini with no monitor

The Setup: iMac (Late 2012) with no peripherals hooked up and a Mac Mini (Late 2012) with no monitor and several daisy chained thunderbolt peripherals, both machines on the same gigabit network.

The Goal: To use Screen Sharing from the iMac to the Mac Mini to remote in to the Mac Mini whenever needed.

The Problem: The Mac Mini display only allows up to 1680x1050 and I expect this is because no monitor is attached. If I attach a monitor or connect it via Thunderbolt to the iMac for Target Display Mode, the Mac Mini will find whatever the highest resolution is and will retain those settings even after disconnecting said monitor...until you restart it.

So, I suppose my questions are:

1) Is there any way to trick the Mac Mini (without a monitor) to thinking it has a resolution up to 2560x1440, etc?

2) If not, I wouldn't mind using the iMac as a Thunderbolt display when needed to set the resolution but being that the Mac Mini only has 1 Thunderbolt port and there are like 5 Thunderbolt Drives daisy chained to it, I'd have to keep unmounting/remounting those drives between the iMac and the Mac Mini every time this happens. Any thoughts on how to address this better?

Thanks!