Many thanks for your patience. Whilst I fully empathise with your position, your employment rights in this situation will be rather limited unfortunately. This is solely due to the fact that you have been continuously employed at your place of work for less than 2 years. As a result, you will not be protected against unfair dismissal or constructive dismissal. This means that your employer can dismiss you or force you to leave for more or less any reason, and without following a fair procedure, as long as their decision is not based on discriminatory grounds (i.e. because of gender, race, religion, age, a disability, sexual orientation, etc.) or because you were trying to assert any of your statutory rights (e.g. requesting maternity/paternity leave, etc.).
So in the circumstances you really have no further ammunition to use to your advantage to try and negotiate a larger payout. In fact, until the settlement is formally signed by both parties, it can be withdrawn at any time and to dismiss you all they have to do is pay you your contractual notice period (or a week’s notice if there was no contractual notice in place). That is all they are required to pay you in law to dismiss you in the first 2 years of service so that is a risk you are taking if you try and push them too far when you have no grounds to demand anything extra.
I'm sorry if this is not necessarily the answer you were hoping for, however I do have a duty to be honest and explain the law as it actually stands. This does mean delivering bad news from time to time. I hope you understand and would be happy to provide any further clarification if needed. If you are still satisfied with the level of service you have received I would be grateful if you could please take a second to leave a positive rating by selecting 3, 4 or 5 starts at the top of the page. Thank you