FLR (M) application and TOC (Name Change) After marriage - Kindly help

[SumitP]

Hello, I hope the moderators or other experienced members can guide me on the next steps we can take in applying for FLR (M) application for my wife. I thank you in advance for any suggestions or guidance you can provide.

Background:
1. I am a naturalized British Citizen and my wife travelled on a Spouse visa in Feb-2016 using her Indian passport (passport had her name before marriage). She was given BRP on arrival to UK
2. My wife's initial 2.5 years of visa will expire in last week of Oct-18. Both of us work in UK full time and we meet financial requirements for FLR (M)
3. We changed my wife's name on her passport on 18-May this year and she now has Indian passport with her name after marriage but BRP with name before marriage

Problem:
1. We realized quite late that we need to inform Home office of any name changes within 3 months of the change taking effect. We cross this 3 month duration on 18-Aug this year
2. On calling Home office, we were told that we can include the name change application on a cover letter as part of FLR (M) application
3. We are unfortunately not getting a premium service appointment until September so combining FLR (M) and name change will mean we breach 3 month duration to inform about name change. Premium service appointments for TOC application also are not available until September first week.

We are looking for help to find answers to below questions:
1. How likely is it that HO will reject FLR ( M ) application if we combine name change with the visa extension together in September (more than 3 months after change of name on passport)?

2. If we send the TOC application for name change separately now, how long does it usually take to be processed and new BRP issued? We will need to book Premium service appointment for FLR (M) accordingly

3. Do we need to have deedpoll for changing name after marriage or just Indian passport with new name and marriage certificate are sufficient along with current BRP for TOC application?

4. On the FLR (M) form, we are including current BRP number so we can secure an appointment before her visa runs out. But this BRP number will change because of TOC application, is the extension request likely to be rejected if the BRP on form and actual BRP number varies?