Is there any solid statement on the home office website that could support this route?
The Home Office is never going to publish a statement indicating that holders of visitor visas can switch to anything withing the UK.
For your question, there is theory and practice.
In theory, when someone applies under an EEA route within the UK, his original status it not taken into consideration. That's why even undocumented people manage to apply for EEA cards within the UK once married to an EEA national.
Now, while the Home Office may show some leniency towards someone who became an undocumented migrant following complex and unforeseen life events, they are less sympathetic to people who enter with a tourist visa, lie during their application, lie to the ECO at the airport, then once inside fill an application. Therefore, such application would come after a string of misrepresentations that undermines its credibility.
Also, not your fault, but there have been a long string of abuse involving the triangle Egypt - Eastern EEA countries and the UK. I mean EEA ladies met on touristic resorts, marry (often for money) Egyptians already married in Egypt, for the sole purpose of allowing them to come to the UK using EEA routes.
I am not implying your relationship is of this nature. But it is within a known pattern and any Caseworker would look at it very very carefully. It is not to the Caseworker to demonstrate that the relationship is not genuine. The burden of proof lies on your shoulders: it's up to you to prove that the relationship is genuine.
This means, if you start your history with UK by lying to an ECO at Heathrow, you are going to help the Home Office in building a strong refusal case against you. They will doubt your credibility and the credibility of your partner.
Never ever under any circumstances lie to immigration authorities in the UK. Once you do, you can't take it back and they have more than enough resources to make you regret it.
Follow the normal process and apply within Egypt and expect the relationship to be questioned.
