If I was doing this design, I would build the fins from lower and taper pocket the bottom edge with a 45° pocket that enables them to print unsupported. It is possible to just leave a gap, or make a single wall riser near the tip to anchor the bridge but this will need printer and materials tuning with inconsistent results in my opinion. I think he was mostly showing off the abstract application of an unexpected idea people are likely to watch.

Ironing is as much about hardness as it is about smoothness. The extended heating will make the lower surface harder and might be workable on your home machine. Your flow rate in slicer settings will be critical for ironing because any bulldozing of material left behind will wreck you. Plus all that extra heat in a solid stack of layers is going to strongly promote warping.

If you’re really tight on clearance for something like this, I have used typical glue stick. You just add a print pause and either some tape or very carefully apply glue stick just to the overhang clearance with a 2 print layer height gap. The glue may take a day of soaking in water or alcohol to completely soften and dissolve, but that is basically poor-person dissolvable print supports. That trick is really only worth doing for stuff like mechanical prints you want to embed in an assembly with tight clearance. It is a pain in the ass and certainly not a transferable design for a farm or file sharing.