It's not your T you have to satisfy. It's yourself that benefits from the processing. It wouldn't do much good if you satisfied your T but were still unsatisfied yourself.

For things that are stuck, we may need additional help with processing. My T uses EMDR for that purpose. He says it is faster and that he prefers to help clients quickly (if they are up to it). He said that with EMDR he can help clients in a fraction of the time it would take with regular talk therapy (maybe years) and he hates to see clients suffer for so long.

It sounds like you don't want to spend 6 months crying everyday in therapy but are ready to move more quickly. How about asking your T how she can help you more quickly instead of the slow route? Maybe you could try EMDR, which is supposed to shake difficult memories loose so they can be more readily processed. If she doesn't do that technique, you could get a referral to someone who does. Or your T may have other techniques she can use with you if she is not trained in that one. There are a number of techniques that can facilitate processing.

I agree very much with what SAWE wrote about doing this work with another person. Journaling helped me process a lot too, but doing trauma work with T was very different from trying to heal all on my own. Our work together reached a deeper place.

I think it would be very helpful to you to discuss with your T the benefits of what she is suggesting, how it is supposed to work, and alternative approaches. And maybe just give what she suggests a go for a few sessions. You think that sitting together with T while you cry about your past and feel your pain and grief will not help. But maybe it will.