Some suggestions... To minimize thermal drift, you should try integrated bipolar transistor quads for the input and input bias transistors, such as THAT340P, or at least duals such as SSM2210 / SSM2220. Make sure the integrated transistors are arranged symmetric across the inputs so as to provide balanced temperature drifts which cancel. For example: one integrated quad for the inputs Q2, Q3, Q9, Q10 and second quad for the bias Q's. That will keep the junctions thermally matched as well as anyone could hope for. Low TC or matched TC resistors for R1, R3, R5, R8 will help ensure consistent reference currents.
Then you have to deal with whatever fixed offset remains. A little trim network could be used to replace the ground connection from the emitters of Q1 / Q4. Something like a high-ratio resistor divider from a potentiometer tied between the rails might work.
Then you'll need a sensitive voltmeter to measure the offset and characterize the temperature drift.
You could also ovenize the circuit... sounds crazy, but it's really not that
(gotta love Wenzel's personal site - some real jewels in there).
I think if you really wanna do it, super low DC offset can be done.