How to make Linux application (all in one fille) installer?

Just use makeself, it creates a shell script with an included archive and can run commands after extraction.

If you need only a self-extracting archive, you can use shar.

e.g.

shar -z -t files/ > bundle.sh

Create a package for each targeted distribution. "One file installer containing the bathtub and the kitchen sink, in case they aren't installed already" is very bad manners. Perhaps this is relevant here.

Distributions have widely different policies on what to ship, configuration file standards, and how to package software. Better recruit some interested party knowledeable with the distribution, and have them take over the packaging and integrating into the distribution. That will reduce friction enormously.