First of, a big thank you to everyone who chimed in on this thread and offered advice! After considering everything, I decided to not only redo the layout, but change components - most importantly replace the feed-in and Cout electrolytics with ceramic caps, and use a different IC. I decided to go with a triple output buck switching converter, actual part is A4490 from Allegro (manufacturer link
https://www.allegromicro.com/en/Products/Regulators-And-Lighting/Multiple-Output-Regulators/A4490.aspx). It looks like a very interesting part and I found it easy to design with. So I would appreciate it very much, if you would look at the attached screenshots of the new design and offer comments and critique, if you see anything wrong...
A couple of things of note: One, the datasheet advises to minimize the ground loop between feed-in caps, inductor, flyback diode and output caps; and to preferably put the flyback diode on the back side of the board - so I used a lot of via stiching alongside attempting optimal placement. Two, the bottom copper is mainly ground pour, but every free square inch on the top will be ground pour as well. Hopefully, with a bit more via stitching, the current will find a short un-obstructed path out... Lastly, just in case anyone wonders, there is a big solder mask region on the bottom side under the converter IC, in order to leave the copper bare - for thermal dissipation. It is not much wider than the chip, since it is constrained by the diodes and traces, but it is tall, about 4x-5x the width of the chip.
And while on the last point... The datasheet lists a few recommendations on page 14 about the board layout, mainly to reduce the GND loop between Cin, D, L, and Cout. Here is my question: As it is, I have placed the flyback diodes closest to the IC, rather than the respective inductor - is this better than placing them closer to the inductor, or should I move them?
As always, thank you all for taking the time to read, contribute and help out!