Uri:
Basically the side labeled for DVD and CD player on the HTS has the most filtering. The other side has much less i.e. where the AMP labeled outlet is and provides for more power hungry applications like AMP.
Based on your comments by all means invest in two dedicated lines, cost for labor will be almost equal than doing just one. As you noticed the less other things plugged in your system's line the better results you get. For quite a while I had my digital source, preamp, amp, TV set, cable signal , VHS in the HTS. I tweaked my system and found a testing track like track #23 in Chesky's "Ultimate Demo disk" and listened to how detailed and better presence the organ sounded and also how better or worse the different part of the chorus were portraited. This led me to just leave in the HTS what I really need for music reproduction, in other words even just having other things plugged there and not "on" had some effect. In your case I'd suggest trying without the Scott and deck and see what happens.
Power cords have also helped me a lot, I even changed the stock in the HTS..... not easy but doable Your comments please
Luis