The input Voffset of 5 mV may be a problem. Since you have a DC gain of 330 in the second stage, that offset will be multiplied by 330 to give you around 1.6 volts in the worst case. There are a couple of ways to deal with this. One is to AC couple at the output at a very low cutoff frequency, but of course this would totally mess things up if you really want a DC response in your application. Another thing you can do is to sum a bit of additional voltage into the input of the second stage to compensate for the offset voltage of the op amp. This is usually done with a simple voltage divider from +supply to -supply which is tapped somewhere near the middle, maybe with a pot, and fed into the inverting input alongside your 1K input resistor. The voltage divider uses higher values than your feedback resistor 330K so that the DC gain from this network is low. The problem with this idea is that it doesn't correct for offset voltage drift vs temperature. The other problem is that your circuit suddenly becomes sensitive to DC voltage drift of your supply rails, subverting the PSRR of the op amp. Another solution is to choose an op amp that has much lower input Voffset.
By the way, those values of input bias current are so low that we don't need to worry about that too much. But be careful when you use such high value input resistors. 10 Mohms is very high. A little bit of humidity condensing on the pcb will mess that up. Another practical problem is that the leakage current of your shunt capacitor may be too high for that 10 Mohm resistance.