Try just a slight lean forward. Tuck your chin untill it almost touches your neck. Dont let you upper arms go past the parallel position. Contract you chest muscles on the lower portion of your dips.
Think of it this way you cant really flex you upper and lower pecs separate from each other.
There are two main part of the pecs.The Sternal major. Thats your big part of your chest. Here is a link
The sternal Clavicular. Thast the upper pecs. It is also just a smaller part when you compare it to the sternal part. Here is another link
But you probably know that anyway. I thought the pictures would give you an idea.
Here is some thing different to try if you can.
McRoberts put out a book a long time ago showing a way to do dips.
If your bars are high enough he says to straighten your legs. Dont let your arms go past parallel. Very slightly Touch your feet on the floor,or a small box,even books so your arms dont go to low. How ever you do it so your arms dont go past parallel.Tuck your chin almost touching your neck.
Some times instead of hanging weights from a chain I would but them in a back pack and were it on my back. This could help the if you have a problem with the weights swinging from a chain. It was a killer in my superslow days.
My dip bars were v-shaped on a stand with a bar attached to a smith machine.
Im not trying any one here how to train or you how to do dips. Just want to help if I can.
Dont worry about your pecs. You should be fine. Hope this helps.
Give it a try.