It is "have been". It is basically never correct to say "am been", and it wouldn't mean what you want it to mean anyway.

One possible, correct sentence is:

I have been, for a short time, an employee of that company.

Or (this is more natural for me, but arguably less correct):

I have, for a short time, been an employee of that company.

Either way, it means the same. It says that you were employed a short time ago. It doesn't mean you're about to leave. I see why you might want "from" in this case, and not "for", but don't panic: in this case, "for" does not mean that it will only be "for a short time"! Just that it is "a short time" so far.

Now, you said you didn't want a grammatical or technical explanation, so we can stop there. But in case anyone else wants to know the grammar behind it, I'd like to elaborate a bit anyway.

A construction like "have been" is called the present perfect. It is for actions that are past and finished, at this moment. Its structure is have + past participle.

(There is also a past perfect, which is for actions that were already past and finished at some previous time. Its structure is had + past participle.)

A construction like "am being" is called the present continuous. It is for actions that are happening (right now), or that often happen (not necessarily right now, but before now and, we expect, after now too). Its structure is be + present participle.

But "to be" leads a complex existence. It is also used in ways that are basically unrelated to the present continuous.

A construction like "am been" is called the present passive. It is for actions where the subject ("I", in "I am been") is the recipient or target of the action. Its structure is be + past participle. You might say "I am insulted" (someone gave you an insult), or "I am seen" (someone saw you), or "I am blessed" (someone gave you a blessing).

It would be very unusual to say "I am been", though. That would mean someone was being you. If an English speaker really wanted to say that, they would almost certainly use different words.

You want to say that in the past you formed an intention to call Jane, and that intention has persisted into the present because it has never been fulfilled. Look at your options for expressing this:

SIMPLE FORMS

I mean to call Jane.
This form describes your present intention. It says nothing about the past.

I meant to call Jane.
This form describes a completed past intention—the technical term is perfective, which is quite different from "perfect" constructions. It implies that the intention was either fulfilled or dropped. It says nothing about the present.

PROGRESSIVE FORMS

^✲I am meaning to call Jane.
^✲I was meaning to call Jane.
These forms are prohibited in ordinary use, because mean to is a stative verb like know, have, live, and these verbs have the progressive sense "built in". The prohibition is weaker in the past form, which may be employed to specifically exclude the perfective sense: I was meaning to call Jane, but kept forgetting. You'll occasionally find this in colloquial use instead of the perfect progressive: I was meaning to call you.

PERFECT FORMS

I have meant to call Jane.
I had meant to call Jane.
These forms describe an intention held before a present (have) or past (had) Reference Time (RT) which led to some sort of a state which obtains at RT. With mean to it is ordinarily used to cast light on a current situation by pointing to past intention, so it tends to be restricted to formal "forensic" discourse: I have meant to assail the motives of no party, or individual; and if I have, in any instance (of which I am not conscious), departed from my purpose, I regret it. — A. Lincoln.  You could use this in the present context, but the intention would be seen retrospectively, and the second clause should be recast to suit it: "I have meant to call Jane, but have repeatedly forgotten to." It would neither imply nor exclude the persistence of your intention into the present.

PERFECT PROGRESSIVE FORMS

I have been meaning to call Jane.
I had been meaning to call Jane.
These are the forms ordinarily employed in both formal and informal registers to express an intention formed before the (present or past) RT and persisting into RT. The perfect piece of the construction (have/had) expresses the existence of the intention before RT, and the progressive piece (BE -ing) expresses persistence, excluding perfectivity.

Incidentally, mean to (as opposed to bare mean) is one of a class of verbs which act as semi-auxiliaries—the to means that they take a to-infinitive.

get to
happen to
have to
seem to
tend to
turn out to
used to
be about to
be going to
be likely to
be supposed to

Each of these follows its own set of 'rules', depending on its semantic character.