Following up on my post, for future reference:
There is a description of Per Monitor V2 here
Warning: The Per Monitor V2 (and many of the other High-DPI features in Windows) have no support for the MDI child windows model. Microsoft has stopped addressing bugs reported for MDI, and we recommend migrating to a different multi-windows model (multiple floating windows, docked panes, tabbed windows, etc.)
I have been able to reproduce the MDI sizing issue with a basic sample MDI C++ application that has the permonitorv2 setting enabled in its manifest. So, as far as I can tell, it is not specific to how mIRC has implemented its MDI support. With this application, and mIRC, when an MDI window is maximized on a monitor that has 125% DPI enabled, and with only some resolutions, the window is sized incorrectly and the caption is actually visible.
There is a solution that involves hiding the MDI window caption when the window is maximized but it results in a fair bit of flickering. If I can find a way around it that works smoothly, I will use it.
That said, seeing that Microsoft has deprecated MDI, the only long-term solution may be to move away from MDI.