Switch from Tier 2 to Global Talent Visa - Existing or New Employer?

I am currently facing a Dilemma regarding making a series of right choices. Let me first explain my situation before specifically asking the questions.

I am currently on Tier 2 Work Visa, sponsored by a UK University, for an academic position (Senior Lecturer). My wife and kids are on Tier 2 Dependent visa. We have already spent three years on Tier 2 visas in the UK. One of my friends recently told me about Global Talent Visa. I have already requested HR to issue me "Statement of Guarantee" letter so that I can initiate the Endorsement (Stage 1) of the visa process. In parallel, I have also received a conditional job offer from another university, similar title but better grade, although the offer is still not accepted.

As per contract I need to give three months notice to my current employer. I am not sure, at this stage, that my new employer will issue "Statement of Guarantee" letter or not to enable me to obtain Global Talent Visa due to any reason (I know some universities do not issue this letter to their employees). Also, one of the pre-employment conditions of my potential new employer is to get reference from my current line manager. This process will start as soon as I will accept the conditional offer of appointment. I do not want to tell anything to my current employer until my visa issue is resolved. I only want to inform them about change of job at the time of resignation or just before giving the resignation. The visa processing can take at least one to two months time (plus potential COVID restrictions related delay), plus three months resignation notice period - I don't want to tell them I am leaving the organisation about six months before I leave it - the general work environment is unfortunately not good.

Now what is the best way forward for me?

[1] Shall I inform my new employer that I am in the visa change process (from Tier 2 to Global Talent Visa) and it is expected to take two months. Once the visa will change then they can start the reference check, etc. process. At that time, I can inform my current employer about my intention to move to elsewhere. Once the new employer confirm that the reference process has completed, I can then resign. Am I right in thinking, although I will get my global talent visa due to the letter issue by the current employer, but I would have not issue in changing my employer by holding the same visa?

[2] Alternatively, I check from the new employer. If they issue me a "Statement of Guarantee" letter, then I accept the offer and inform my current line manager about my intention to resign. Once I get the endorsement and subsequently received the visa then I resign from my current position and serve the notice period. Can I complete the notice period with the current employer, despite being on a visa issued due to the letter issued by the new employer?

[3] I have already completed three years and two months on Tier 2. I am now switching to global talent visa. What is the right time and process for me to apply for ILR. I understand my family members have to complete full five years before being eligible to apply for ILR.

Any guidance you can provide would be greatly appreciated.

Can anyone respond to my query please? This is urgent.