Using alternates. View by clicking "character set." Width compressed by user.

The Criterion reissue in 2020 included a bonus disc with plenty of text set in the Jarmusch font. For example, here is one that discusses RZA, who composed the soundtrack.

I couldn't find a close substitute but I trust that among the vast number of handwriting fonts at least one of them might work as an approximation.
Does anyone have a suggestion?

Did not find an exact match.
Times Now ExtraLight is similar.

The titles were designed by Balsmeyer & Everett Inc. The titles are set in a custom font based on Jim Jarmusch’s handwriting.
For more info see
http://annyas.com/screenshots/updates/ghost-dog-way-of-the-samurai-1999-jim-jarmusch/

Custom numbers for the barcode.
Looks like it's based on an old metal typeface, Ludlow Tempo Medium of 1930.

Serifs added to _1_, _2_, _4_ and _7_. More curve in _6_ and _9_.
Not digitized except for an unsatisfactory Grunge version by Steve Jackaman

Agree there does not seem to be a digital version.
Closest for most letters might be a Garamond, such as Bitstream's Elegant Garamond. But serifs are not as pronounced. _P_ has a gap and _C_ lacks the serifs. Similar _C_ found in Baskerville and Bodoni.

PUSH looks like the letters below, but with width expanded about 200%.
They seem to match Six Caps by Vernon Adams:

Six Caps is a free font with an Open Font License Copyright (c) 2011, by Vernon Adams (vern@newtypography.co.uk)

Christian Robertson is now a designer for Google -- notably Roboto.
He has published some pro versions of his fonts on My Fonts.
Possibly he will do this with Calla Titling.

Sorry didn't mean to jostle you. But I kept digging and the answer popped up.

Calla Titling was designed by Christian Robertson at Beta Type. Was sold through Veer which has been defunct since 2016. Specimen shown in a Klingspor Museum pdf:

http://www.klingspor-museum.de/KlingsporKuenstler/Schriftdesigner/Robertson/ChristianRobertson.pdf

Custom leg on _R_. Pointed tip on _A_.

Custom script lettering for car nameplate. A few fonts are similar, but not a match, including Citadel Script

Bayside, sold as part of the Hoefler Numbers set.

According to Hoefler: Bayside is an adaptation of those delightfully eccentric house numbers that are native to suburban America. Their bizarre forms recall the “chinoiserie” of the Aesthetic Movement, a nineteenth century fashion whose romance with foreign influences wasn’t especially concerned with historical accuracy. Bayside’s forms are based on a set of numbers produced around 1928 by H. W. Knight & Son of Seneca Falls, New York. Widely copied by other manufacturers, these forms have gradually softened over the years; Bayside restores them to their loopy grandeur.

Your numbers are a later version and show minor differences from Bayside.

These were common in the US and Canada around 60 years ago. Here is a full set.

The _1_ can be used with the top and bottom reversed.
AFAIK they have not been made into a font.

Presumably address numbers. The curved thick to thin strokes are similar to "wonton" fake Chinese, such as Sudoku here at Dafont.

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Looks like the 1960s psychedelic poster lettering of Californian artist Rick Griffin.
It inspired the font Rick Griffin.