Screen Sharing, increasing resolution

At work, I have a Mac mini (2012), connected to a 21" monitor running at 1920x1080.

I also have at work a Windows 10 machine (WinBox), similarly running a 1920x1080 monitor.

At home, I have a 27" iMac running at 2560x1440, with which I connect to the work machines using Screen Sharing (to the mini) and Microsoft Remote Desktop (MRD, the WinBox).

When I log into the WinBox with MRD, it does some magic with the display subsystem to give me a remote Windows display with the full resolution of my 27" iMac, 2560x1440, even though the physical 21" monitor at work only runs at 1920x1080 when logged in locally there. This is generally very useful.

When I log into the mini with Screen Sharing, I only get a window with the resolution of the mini's account, 1920x1080, and there seems to be no way to increase it. I tried a second account on the mini to try and get a virtual display instead of sharing that of the logged-in account, with no better luck.

The 2012 mini should support up to 2560x1600 on the Thunderbolt/DisplayPort that the primary 21" monitor is connected to, but the 21" presumably doesn't support anything over 1920x1080, and apparently that monitor controls the resolutions offered to Screen Sharing, even with a separate account.

Short of attaching a different monitor to the mini's video port that does support 2560x1440, is there any good way to get that resolution over Screen Sharing onto my iMac? Or a not-too-hacky and not-horribly-expensive alternative to Screen Sharing?