Couple of things - as a practical matter its a moot point whether or not you use the tape or aux input, you really can't use the tape in for whatever reason. Your only pratical recourse is to use the aux input which would be the same as any other input on the unit (except the tape). In veiw of the compromises you are already making I wouldn't be too anal about the results. Enjoy what you've got until you get a dedicated headphone amp whcih should be a huge improvement for you.
I suspect the -20db circuit yopu mentioned appears before the amplifying stage of the pre-amp is intended more as a quick volume reducer, similar to a mute circuit but not as severe, that folks would engage to enable them to talk, answer the phone etc, leaving on some background low level sound. It would probably not be my first choice as a way to reduce the volume when you use the tape in. But, you have at hand the means to evaluate the differences in the various ways. Just pick which sound best to you.
I suspect the -20db circuit yopu mentioned appears before the amplifying stage of the pre-amp is intended more as a quick volume reducer, similar to a mute circuit but not as severe, that folks would engage to enable them to talk, answer the phone etc, leaving on some background low level sound. It would probably not be my first choice as a way to reduce the volume when you use the tape in. But, you have at hand the means to evaluate the differences in the various ways. Just pick which sound best to you.