Certificate correction - timing, contact HO ?

My citizenship certificate had a mistake (misspelled place of birth), which was clearly HO mistake (I entered the correct name of my birth city on my naturalisation application, and it is a well-known large city).
I sent the certificate back for correction, together with their form and appropriate page from my naturalisation application, where I had correct city spelling (no payment, as it is their mistake, and anyway they say they will ask for payment if needed).

It was about 7 weeks ago. They do say that "it might take up to 12 weeks", but I really need it, as I need to apply for passport.
It looks like most people get it back in about 4 weeks - but I saw some horror stories on the net of people waiting for more than a year..

I am EU and for now can travel on EU documents, but I will need to be mostly in Europe for about a year starting rather soon - jobs reasons, and I will change my UK address, etc. - so I am concerned that certificate might not arrive on time to apply for UK passport from UK, and/or that it will arrive after I change address..

Is there any phone number or other way to contact HO about certificate correction timeline?

I sent certificate to the address on their form:
Department 201
UK Visas and Immigration Silver Zone, 4th Floor
The Capital
New Hall Place
Liverpool
L3 9P

Is there alternative way?
For example, if I do not get correction on time and will try to apply for replacement certificate, will it come with the same mistake?

These are the contact details from gov.uk (remember it's just a call centre and not the case workers)
Citizenship and nationality enquiries
nationalityenquiries@homeoffice.gov.uk
Telephone: 0300 123 2253
Monday to Thursday, 9am to 4:45pm
Friday, 9am to 4:30pm

So: I sent them both email and a regular mail to the same address where I sent certificate.
Yesterday, on Thursday 5/06 I received a call from HO - they said they just got to deal with my request, amended certificate and sent it back on Wednesday 4/06 (they even apologised for delay). Today, on 6/03 I received my certificate back. Seems like everything is correct.
So it took them about 9 weeks. Not sure whether my enquiry sped up the process, probably yes.