Yep, that's it precisely. Well done everyone. I've added my (almost identical) solution video to the workshop page or you can have a look here:
SOLUTION
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Xtreger deserves the credit for the initial cube fling which appeared almost identically in his map "Trifurcated" as one of two intended methods. I just added the slime moat and the 90-degree turn which makes everything nice and tidy.
Also, thanks to marKiu for mentioning something about wall buttons which apparently stuck in my mind.

Oh! So you can get the funnel from up top. I'm not sure how I missed that; that led me astray all day. And I can't believe I got more or less correct the method of getting the cube up to the top. I thought for sure that was unintended and spent a lot of time looking for an alternative.

Very nice map. Very well thought out. Definitely not for your average Portal player.

Yeah you had it right the first time. You should believe Marc when he says that it sounds like my style. That ending sequence was a very interesting PTI experience for me. Just improvised in the last hour or two of map making. As you can see, it's crucial that you can see the funnel portal from near the laser field, but not from any higher up. Otherwise you would be able to arrange the cubes downstairs and not need to manipulate them from upstairs. Thanks again for playing!

So your reason for putting in the timer was just to make me (and others) think I had the wrong solution? Or did I miss something else?

No the reason for the timer was that your described solution had you shooting the portal on the floor under the relay and then picking up the cube to hold against the wall button, opening the upper fizzler at the last moment. My only problem with that is that it skips the idea that you can crouch and balance the cube between your head and the wall button, allowing you to then turn and fire portals. The timer makes this necessary, although in CF's solution he appears to be standing? I couldn't make that work myself but it's easy if you crouch.

My third PTI map is released here: PeTIte [three]