Ghosted by UC, including complaints department - any advice?

Hello - I’m having difficulty getting any kind of response from UC about a client having her child added onto the claim and the child element paid. It’s a very non controversial issue, and I’ve not experienced UC not responding at all to anything, particularly when it’s not a complicated argument..! Would really appreciate any advice as to how else this can be escalated, I’ve put a chronology below in case useful.

11/03 - birth of child
15/03 - change of circumstances reported
15/03 - I left a message on her UC journal with her explicit consent asking for an upload link for her to provide evidence of change ASAP whilst immediately postpartum
19/03 - I left a message on her UC journal with her explicit consent reiterating the previous message
19/03 - I emailed the Service Centre mentioned on her journal to escalate this, in order to receive a response via her journal
22/03 - client and I called the UC helpline on 22/03 and at that point, a customer service agent left a message on her journal and also said that they would flag the situation with her case manager.
26/03 - I left a message on her UC journal with her explicit consent
26/03 - I submitted a complaint online on the client’s behalf
28/03 - I left a message on her UC journal with her explicit consent, requesting a mandatory reconsideration of her latest UC statement which has no child element included
03/04 - annual changes to housing costs completed (as she lives in social housing and her rent has increased as of 01/04)
08/04 - I emailed the relevant area’s National Partnership Team contact, who advised they would contact the relevant Jobcentre
10/04 - a further evidence appointment was booked for 18/04
18/04 - client attends further evidence appointment with all evidence of newborn child
18/04 - I left a message on her UC journal with her explicit consent, requesting an update as to when she will receive an underpayment for the child element, and confirmation that her housing costs (increased as of 01/04) have been verified and will be included in her next payment for the AP including 01/04
24/04 - emailed London and Essex National Partnership Team contact again who said they would contact the Jobcentre again
30/04 - next statement is available as of today, which includes the child element for this month, but not an underpayment for the previous month, nor have her housing costs increased in line with her rent increase - now escalating to Jobcentre team leader, and emailing .(JavaScript must be enabled to view this email address) which the ICE gave as the email address to chase DWP complaints via (though I cannot imagine that email inbox is checked very speedily!)

Hi Zoe

If you want to email me the client details (.(JavaScript must be enabled to view this email address)), I’ll raise it via stakeholders as an example of poor communication - and hopefully that will get it sorted too :)

Zoe,

I think the .(JavaScript must be enabled to view this email address) inbox is checked quite regularly. Reason for thinking this - I sent a complaint email to it last week and forgot to attach my attachments. They got back to me within the hour pointing this out to me.

Jim