Request Advice on ILR Application and Dependent Visa Extension

[hirennc]

Hello,
I am a Global Talent visa holder endorsed by Tech Nation under the exceptional talent route, preparing to apply for Indefinite Leave to Remain (ILR). My child is my dependent Our current visas, valid for three years, expire on 15th September, 2023, which is also when I become eligible for ILR. Please also note my partner is on a independent and separate GT - ART category visa holder and eligible for ILR in Sep 2025.
Given the 28-day window for ILR application and my child's visa extension, I am seeking guidance on:
1. The optimal sequence for these applications - should I apply for ILR first followed by my child's visa extension or can these be done simultaneously?
2. Ways to circumvent the potential issue of unavailability of priority services (excluding super priority), which might lead to extensive waiting times. I understand many people are not offered priority dates.
3. Any helpful links or resources for the application process.
Your advice would be invaluable. Thank you in advance.
Best regards, Thx