As I already mentioned, any initial appeal, no matter how clear you try to make it, is going to be rejected. So, with that in mind, whatever you send is going to bee a wasted effort.
As SIP are IPC members, their offer of a secondary appeal to the IAS will be about as useful as a poke in the arm with a sharp stick. Personally, I wouldn't bother with an IAS appeal although others on here will disagree. The choice is yours.
Where this will ultimately be settled is if it is referred to the county court as a small claim. No one who is here receiving advice and following it pays a penny to the likes of SIP. Any claim, if they even try to take this that far, will either be struck out or discontinued. Even if you were to be one of the less than 1% that were ever to get as far as an actual hearing, you'd be likely to win anyway.
It's up to you how you want to proceed. But thigh the above in mind, you make your choice. The appeal you have shown is clear and follows logic. It's a pity that SIP and the IAS don't.