@Topoftheroof - What you are doing in being a kinship carer for four children is absolutely brilliant. I used to work with someone who was doing the same for her brothers children - she took one on and then ended up with three! It is definitely something to be admired.
However, just because it is a kind and altruistic thing to do, doesn't mean that you should be put at a financial disadvantage, so have you checked that you are getting all of the fostering allowances and fees that you are entitled to?
As an absolute minimum you should be getting £170 per week per child in allowances and £165 per week per child in fees (although most LAs pay more than this). That's just under £6k a month for four children and should be tax free.
On top of this you may be able to claim universal credit as fostering allowances are not counted for the purposes of assessing UC claims.
If the LA are not asking you to stop working full time as part of the child's care plan, you are also entitled to free child-care which may increase the hours you are available to work.
Also - do you live in the same LA that have responsibility for the children? If so, check to see if they waive council tax for foster carers - many LAs do. If you don't live in the same LA or your LA doesn't offer it as standard, push for it anyway and check what else you may be able to claim for from them. Remember it would cost them a whole lot more to have to place four children in an external placement than with you and LAs do have some ability to pay additional discretionary expenses, if it means being able to keep the children in Kinship care rather than having to tie up an in-house carer or pay an IFA.
If you are going to go down the SGO route, check whether the LA offers parity and will continue to pay fees and allowances at the same level as the fostering fees and for how long (some LAs are now doing this until the child leaves care or turns 18). While SGO would absolutely be the best thing for the children, don't yield to the pressure to accept it if they won't continue the payments until the children are at least in school full time and you can return to work.
Speak to the Fostering Network and Fosterline and get their advice and support - they will be much better placed that randoms on Mumsnet to advise how to best approach you employer.
Speak to your employer about becoming a Foster Friendly organisation (https://www.thefosteringnetwork.org.uk/get-involved/fostering-friendly-employers/) - they may be willing to offer you some flexibility without having to formally go down to two days a week (shorter days / home working combined with free childcare) or some other flexibility around this