How to figure out a tone center in an ambiguous/chromatic situations?

The general answer

To start, it's worth making a distinction between a tone center and a pitch center. I infer from your use of "tone center" that you're looking for a "tonic" pitch -- that is, "what key/mode am I in?"

Nevertheless, one way to attempt to figure out the key and mode is simply to take each unique pitch in your piece, place them in pitch-ascending order starting from what you perceive to the the "primary" pitch, and see what you get. Of course, if you have too few pitches you might get nothing, and if you have too many, you just get a chromatic scale.

By definition, an ambiguous or sufficiently chromatic musical passage doesn't have a tonal center. It might have a "pitch center" -- that is, a pitch that the listener perceives as a stable point or point of focus -- but not be in a key.

For example, Ligeti's Musica Ricercata, no. 1, has a clear pitch center -- A -- but it cannot be said to be "in the key of" anything.

But you can force a tonal center on otherwise ambiguous situation.

The melody of Samuel Barber's "Nocturne", op. 13 no. 4 is built on a twelve-tone row, so has no pitch center. However, by embedding the twelve-tone melody in a tonal-sounding harmony, the whole piece winds up sounding like Ab Major. The piece stands up to a twelve-tone interpretation in a very clear and logical way, but woe to the person attempting a tonal analysis without stretching the rules to meaninglessness.

Toward a specific answer

I think your composition is sufficiently ambiguous so as to say it doesn't have a tonal center, but certainly E and A are candidates for pitch center.

You've built (this part of) your piece around two musical ideas: 1) a "chord" (maybe better to call it a "simultaneity") consisting of the pitches F# G and A, plus E and/or Bb, and 2) a three-note chromatic cell, always descending, sometimes transposed.

As is, I hear your piece with E as the pitch center. But I like the sound of Bb in the bass against the chord-centric moments, "resolving" to an A in the bass against the chromatic moments. To my ear, that gives the E a sort of "dominant" feel, and the A a "tonic" feel. If placed in rhythmically interesting places, I think those two pitches alone would give a pretty cool sound, maybe like a funky A minor. Now that I think about it, let's apply the suggestion above of ordering the pitches. The scale would look something like A Bb [C D] E F# G, which, ta-da!, is second mode of G melodic minor. (C and D are in brackets, because you don't use those pitches in a significant way.)

You might consider making the piece even more rhythmically ambiguous, to go with the tonal ambiguity. You can do that by having the bass play at irregular intervals. That would still be compatible with the Bb - A suggestion if you like it.

Etc., etc., etc. ...