pu/pd is pick up put down, where you pick them up to comfort them when they get upset after being put down for a nap, then you put them back down again and leave them for a bit. You continue the cycle till they realise that its time for sleep.
It didnt work with mine as you cant pick up 2 babies at once!
Sorry to say, but you may have to try one of the 'harder' methods to see results in the long term. If she is 7.5 months and has always goen to sleep on the breast then she is going to find it very difficult to self settle. You may need to spend some time working with different methods. Some fo those are pu/pd, shush pat - this is the one I used. I used to sit between their cots and pat their bottoms (where they liked but can do chests etc) and shush until they were nearly asleep. We dont have to do this now - or controlled crying is another that works for many, but not all. It wouldnt work for us as the boys would work eachother up so that they were both howling and I couldnt comfort them together on my own (hubby works long hours).
You might need to tweak your bedtime routine a little. When the boys were small I used to give them a bottle, bath them and then put them down. Now they have a bath, then bottle, then watch ITNG and have a story before bed. This way, although they do drift off when having their bottle, they never went to bed on it.
Hope you find a solution soon xxx