What is a good way to add a programable offset to a diffential signal?
I'm unsure of how the signal is ground-referenced at all, but if you want OA1 to get a DC signal added to its inputs, current sources
of opposite signs applied to the terminals of R4 should
accomplish that.

Two sections of LM13700 (each is an operational transconductance amp)
can be programmed with matching (circa 1 mA) current sources and
connected to a +/- 1V trim input, one section having the trim
to its (+) input pin, the other to its (-) pin (ground the other
input pins).  The two outputs
are then complementary currents, and can be applied to the two
ends of the R4 resistor.   These are current source outputs; a choke
in series will prevent signal loading even at high frequency.

To get higher offsets, some resistor changes in the input
circuitry might be required.