I would arrange meeting with HR asap. Tell them you are seriously considering redundancy option because of A B and C
Asking them if you accepted redundancy would you be able to look for another job straight away and when would you be allowed to leave the company.
Get it on file, in writing, recorded or whatever and take the money. Most companies offer 1 weeks pay for each year worked as a bare minimum so 8 weeks pay is much better in your pocket than theirs. Most large firms also have a pot of money for redundancies/restructuring so i cant see you having any issues.
In my opinion you would be throwing away money by sorting another job out first and handing your notice in as you will get didly squatt and they may make you work the full notice period if they are that way inclined. If you take redundancy they may let you leave immediatly