To start, I agree with Mirlan. I think most likely the final chord should be written as a Fm7add11, but I wanted to add a few more things.
For reference, chords are named using something called tertian harmony, which is the practice of using stacks of thirds to create chords. Generally speaking, the smallest most complete stack of thirds is used to name a chord. For example, if you had a C-E-A, you would call that an Am not a Cadd13. This gives an order of importance for scale degrees when naming chords, namely 1-3-5-7-9(2)-11(4)-13(6). However, this is not always true. Mirlan gives the example of omitting the 5th, a practice common especially in jazz.
With that all in mind, I'll break down how I think you could name the chords in your progression.
E♭-G-B♭-E♭: Agreed, definitely an E♭ chord
G-F-B♭-D: I incline to agree with the software in this case. This has all the notes of a Gm7 and is played in root position. Further, from the perspective of functional harmony (see video), Gm7 has tonic function (disputed), same as E♭. Whereas, B♭ has dominate function as the V chord. Functional harmony dictates that a dominant chord should be preceded by a subdominant chord.
Your interpretation of the chord as a B♭/G isn't necessarily wrong though. First, lots of music works non-functionally. Also, the very fact that you hear the B♭ as the harmony goes to show it is the harmony (tautology, I know). People's ears are usually onto something. How many octaves are between your left and right hands? The farther they are apart the less important the base is to the harmony. How is the bass moving? You could have something happening similar to a walking bass, meaning the bass is less important in defining the harmony (the base can play notes outside the chord).
There is also a third option, which would be that the chord should be written as B♭6/G. Writing this basically says, "while the G is important to the harmony B♭ is still the root." This is pretty much halfway between the previous two options.
C-G-B♭-E♭: Almost the same reasoning as the previous chord applies to this chord. In this case, functional harmony doesn't support either interpretation, Cm7 or E♭ (both serving tonic function). Additionally, it appears that your right-hand voicing for this chord is the same as your one for the E♭. This might mean that the base (left hand) is functioning more as a melody than part of the harmony.
F-A♭-B♭-E♭: Imo, this is the hardest one to name. Strictly by tertian harmony, the chord should be called B♭7sus4 or B♭7sus4/F. There isn't any funny business with that interpretation. It is just a stack of thirds, without any omissions (one suspension). However, it is an inversion which makes it less "solid". Yet, the main reason I think it probably should be called a Fm7add11 is that the B♭ is played in every chord of the progression. This is a solid example of a pivot tone, one note that stays constant. This allows more complex harmony to form without the listener being overwhelmed. In a way, think of the Fm7add11 as an Fm7 with a B♭ played over it.
In all, my guess is that I would write the progression as: E♭-Gm7-E♭/C-Fm7add11, but that certainly could change with more specifics.