As I understand it from your reply and the video you linked to, if a friend in Portugal can write me a letter saying they'll host me for the four month period of the D7 visa, that should suffice to get me the initial visa. Then, once I arrive in Portugal I can then secure a rental agreement in time for my interview at SEF. Does that sound about right?
I completely understand your concerns about the renting unseen etc and the temporary arrangement to give you time to set up something here in time for the SEF interview does seem the ideal solution. An enviable position to be in if it works, I'd say. However...
I'm afraid I'm no wiser than I was about the specific form of evidence you must supply if you're being accommodated in this manner, so whether a simple letter from a friend will suffice or whether it might have to be something more formal, I really don't know. If I had to guess, I'd say probably the latter. If I come across anything else on the subject, I'll let you know.
Also, Gilda did say on that video that different consulates apply different criteria and, with specific reference to such arrangements, that they aren't acceptable to all. She didn't go into any further detail though, other than to say that her consultancy can get information from the individual consulates as to what their specific requirements are.
So unless someone on here has experience with the London consulate on exactly that matter and can shed some light on it, or you can wring the info out of the consulate yourself, you would have to either wing it and hope for the best or (loth though I am to suggest such a thing on an internet forum such as this, where we're all here to help each other for nothing) pay to engage the services of a professional. I guess they won't give away all their trade secrets for free and it might be money well spent if it avoids you chucking money down the drain on a wasted application.