For rendering integer-scaled pixels (of a 240p source) on a 1080p display using the OSSC, there are already a couple of existing options and known limitations as far as future improvements.
Without using an additional device in the chain, your only option is to use line-5X mode with the 1080-line output option (assuming it is compatible with your display). Other than this mode, no other signal the OSSC outputs has 1080 lines, and as a result your 1080p display will always perform scaling, preventing pixel-perfect rendering.
The ability to display a pixel-perfect line-3X or 4X image centered in a 1080p frame (with borders) would require implementing buffering of the frame, which as far as I understand is not possible given the OSSC’s memory size. It furthermore would add lag to the signal, which is undesirable for many (if not most) of the people using the OSSC in the first place.
Your other current option is to put the OSSC’s output through a second device that does perform line buffering, such as a DVDO, Framemeister, XPC-4, etc. Such device will generally cost more than the OSSC and add a frame of lag or more.