I don't have a gizmo, but have a few things you should consider -
All the signals that come through the headphone jack are "processed" through the iPad software, and whatever sound settings that you have - so ideally you want to have the signal go through the 30 pin connector.
If you have digital inputs, it would be better to use these versus analog inputs.
Consider how you have your music stored on your iPad - the average CD album contains about 1/2 GB of data - the average album compressed at 128 Kpbs (default compression of iTunes) and the album is going to be around 25 Mb so your compression is better than 20 X.... So, using an expensive stereo with compressed music is a lot like looking at 640 x 480 jpegs on a high resolution screen.... If you use lossless audio, you will get high quality sound (theoretically same as the CD), but while lossless audio has some compression, it takes up A LOT of space. Why does this matter? Well, if you are using your iPad music as background, and you are using your iTunes library (which I am assuming has standard, or near standard compression)- it won't matter what your solution is, as you should not expect audiophile results - so use the headphone jack, and you will get reasonable sound quality, and you won't spend a lot. If you want audiophile sound - you first need to encode the audio using the lossless option in iTunes, then find a good 30 pin connector to whatever input you prefer using - here is a pinout than any competant electrical person should be able to make a cable for you -
Apple iPod, iPad and iPhone dock Connector Pinout - AllPinouts
For a Tweener solution the Apple AV connector is probably pretty reasonable