Rediscovering feelings from the past is basically the way to integration. You have to re-live things to be put back together and that includes painful memories/feelings that you don't particularly want to remember. I've pretty much re-created my childhood in therapy, with the same feelings, and that has started to put me back together. I'm not fully integrated, but I'm co-conscious. My parts never communicated with each other before therapy but now they do.
Cutting off your feelings is the same as dissociation and the goal is to stop dissociating; to feel again etc. so I can't really see a therapy that supports that, IMO.

Then again, this is your life. Your therapy goals can be whatever you want and if your therapist isn't following the plan you had in mind, find a new one!

(My therapy has been transference based with a combination of CBT/supportive talk therapy, as well as medications and supplements. My therapist is a psychiatrist who has practiced for 50 years, so I trust that he knows what he's doing. However, it has NOT been a smooth road at all. Some periods are quite hellish, to be honest.)