Trying to understand my IR35 status

[WordIsBond]

Based on the facts you've presented in your opening statements, I'd deem you inside because of the Friday - Monday situation that you're in.
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1. Friday-Monday is not automatically inside.

2. Technically it's not Friday-Monday because the company OP was working for on Friday will not be in existence in Monday and OP will be contracting with a third party. A related party, which doesn't help the case, obviously, but not the same party. And the end client will be a company that has never operated a PAYE scheme here in the UK.

If working practices and contract are clearly outside, I personally would ignore the Friday-Monday thing. If it's borderline, then the Friday-Monday would tip the balance.