Migration to UC with WCA awaiting decision

I am Appointee for my 49 year old son with Down's Syndrome. Last month we were sent a migration letter for ESA to UC. Having read the details I realised that changes to his condition reported to DWP office had not been acted on. I wrote to ESA office and they sent a WCA form but didn’t answer my letter. The WCA was received by them 10th Sept but I still haven’t heard back. I am worried about him not receiving the benefits he should. We were told not to apply for PIP (to replace DLA) until we had a letter but now I feel we should apply to speed any correct decisions on UC. I only have until mid November to file the claim form for UC - should I apply for PIP now, as I think he would be assessed as being in a higher category?

I submitted paper version 6th September. Prior to this he had a dreadful face to face assessment in 2014 where the Assessor said he looked depressed, was trembling and had hearing aids - none of which were true! After hanging on for 50 mins I got through to the PIP helpline today. They told me the WCA were taking 6-8 weeks and that if I applied for PIP now and filled out the form they might well take information from the WCA as well to help make a decision. I believe that they are planning on eventually merging the assessments so maybe they are trialing that now with some people. I got through to new requests for PIP in 2 mins. As they are prioritise those applications as well. I decided while my dining room table is covered in documents, information and reports I might as well do the PIP as well!