Can these colours be replicated or captured using ink, paint or traditional film photography?

Ultramarine pigment is too blue for your screen to replicate properly, for example. I don't know if there's a pigment that reflects only 520nm light, though.

Should be.

For printing there was PANTONE's Hexachrome which used 6 ink colours to greatly extend the possible colour range --- but the only printer I know of who made great use of, and profited by doing so, used it only for its increased range's covering of additional spot colours --- so they basically persuaded every printer w/in driving distance to sub-contract spot colour work to them (for those colours which fit in the Hexachrome gamut), then used fancy software to gang up jobs onto a plate, run as many copies as were necessary, cut and stack, and then send out the jobs and run the next plate, no need to wash down the press and change inks.

I tried to sell the idea of implementing it for high-end photo pieces at a printer I worked at, but no real interest because it was difficult for sales to communicate, and no one wanted to spend money printing a sample/researching images which benefited from it.

yes, using a photo printer. with varying levels of price and gamut.

Many colours outside of the electric screen spectrum can be made with ink or paint. You probably have a bunch of objects in your own house with colours that can't be shown as full on your screen.