You are the third person this afternoon asking for this extension, therefore the obvious next task is creating it. One person emailed me this morning asking to paste a url and have the article read to them, and it came up again in another thread here.
Of your two options, I think the forwarding version is the better primitive. Selection is always a possibility, but right clicking on the highlighted text and telling it to forward it to you doesn't require as many parsing heuristics, since the user already told you what they want. Whole page mode could be layered on top as an option with a readability pass.
The panel version is tempting because the reader itself is already a self-contained static app, and would require little modification to appear as a side panel in another app, but then I would have to maintain two apps for little purpose.
The cool thing is that no server is required at all! A content script on readkinetic.com could write directly to the app's indexedDB from your extension in the same origin, so the script merely takes the text from the page you already have open and gives it to the local copy of the reader. Nothing passes through my servers, which is the whole point of the thing.
The embedded version is something I haven't thought about before, but is actually really cool. Using the exact same trick in reverse, the embedded version already exists in the visitors browser, so there isn't a fetch to do at all! The only wrinkle is styling it such that it doesn't get mangled by the host app, hence the shadow dom and small bundle.
Genuinely appreciate your feedback!