You used the THREE mills in parallel, for the 16 ohm R1 value. right? The only way partial bypass can work is when you build R1 using, say TWO 8 ohm resistors IN SERIES to achieve 16 ohms. Then you can bypass just half the R1 resistance if desired.
With a 12dB "PI" pad I've also tried using THREE 8 ohm resistors in SERIES to build R1, then you can bypass 1/3, 2/3. or all 24ohms with a variety of caps, for finer tuning. Won't take long to determine which one provides the best results with the largest percentage of your recordings.
I figure that at least 10 or 20% of all CD's are too damn bright/sybilant with many systems anyway. A slight lack of high end extension is one heck of a lot easier to live with during extended listening than slightly hot, sybilant highs, so I tend to "ear tune" for a little more laid back overall sound.
While you are playing with the 10/12dB pad, trying ANY value between 16 and 25 ohms for R1 is within reason as a means of level adjustment. If 16 is too hot, 25 too cold...ha, maybe 20 ohms will be perfect for you! This is the DIY part where YOU are the number one customer that must be pleased. BTW, ratshack sells a 25 ohm rheostat you might try using as R1 for finding the rough value needed, then install the closest Mills value available.
Whatever you try, don't make more than one, easily reversed modification at a time. And leave well enough alone between tweaks, giving you ears time to acclimate to the "new" sound of each tweak. Try listening to your handiwork FIRST THING in the morning. Sam