OK. If it were me I'd look to tweak that manual Gain control if the output of the API is too hot, but if you're keen to look into pads ...
Great resource:
http://www.uneeda-audio.com/pads/Looking at the Balanced U configuration,
For a 1db Pad : k=10^(1/20) = 1.122, I'd be looking at Rshunt of 10K, so Rseries = 10K * (1.122 - 1) = 1220 ohms, divide by 2 (because in a U pad there are 2 series resistors) gives you 610 ohms, nearest real world value 620 ohms. Working backwards using 620 ohm series resistors, k = 1 + ((2 x 620)/10000) = 1.124, db pad value = 20 x log(k) = 1.015 db. So what you need in the U diagram is a 1% 1/2watt metal film resistors from Jaycar, 10K ohm for R2 and 620 ohm for each the R1/2.
Do the same for a 0.5db Pad and what you get (real world values) is 10000 ohm for R2 and 270 ohm for each the R1/2, giving a theorectical pad value of 0.46 db.
HOWEVER, please take the time to read the article because these values may not deliver what you want when dealing with tiny pad values in the real world. Note in particular the following extract -
Practically speaking, the absolute loss is determined by the parallel combination of the shunt resistor and the input impedance of the mike preamp. Since the preamp bridges the shunt resistor, the actual loss is slightly greater than calculated (less than 1dB). For loss values less than 20 dB, you may have to raise the value of the shunt resistor to make the series resistors large enough to not excessively load the source. In that case, the contribution of the preamp's input impedance to the attenuation error will increase.
In other words, the lower the pad db value, the more the resistor values become subject to the specifics of the equipment involved (the comp and the DA) and less predictable using theoretical formulae!
On the other hand, a pack of eight resistors from Jaycar is 55c, so you are looking at $1.65 plus soldering time to wire up a pad inside an XLR socket and see if it works (put the pad between pins 2 and 3).