The -jmować/-jąć family of verbs

I'm trying to find similarities and differences in verb families.  I find that I get confused with a lot of verbs that have the same roots but different prefix stems.  Today I want to look at verbs that end in -jmować (imperfective aspect) and have perfective paired verbs that end in -jać.

A good primary example of this is:

obejmować, objąć - to embrace, to hug, to grasp; to include, to contain, to encompass

One primary meaning of this verb in English is "to embrace" (hence I have bolded it above), but secondary meanings which can be important to its connotations are also included above.  Another primary meaning is "to include."

The verbal prefix here is "ob(e)-", which means "around, about, of"

Present tense of obejmować (singular 1st, 2nd, 3rd, then plural 1st, 2nd, 3rd):

obejmuję
obejmujesz
obejmuje

obejmujemy
obejmujecie
obejmują

Future tense of objąć (singular 1st, 2nd, 3rd, then plural 1st, 2nd, 3rd):

obejmę
obejmiesz
obejmie

obejmiemy
obejmiecie
obejmą

Imperative: obejmuj (obejmować), obejmij (objąć)

So all the rest of the verbs in the -jmować and -jąć families follow the same conjugation patterns.  Each of the verb pairs means basically the same thing, though one is imperfective aspect and the other is perfective aspect.  With respect to the perfective verb, the "present"-style conjugation is considered future conjugation.

The roots -jmować and -jać appear to have some meaning related to moving, either with the arms, or metaphorically or mentally moving.  It can be inward motion (taking, grabbing, intercepting, accepting) or outward motion (extracting, taking off).  Some of the secondary meanings seem tangentially related to this movement paradigm.

podejmować, podjąć - to take (steps), to make (a decision), to take up (work), to undertake
Verbal prefix is "pod(e)-", "under, below, up to." Or is it "po-" "de-"?  Probably the former since a literal meaning is "to under + take"

pojmować, pojąć - to comprehend, to conceive, to grasp
Verbal prefix is "po-" ("over, through, after, carrying action for a time")

przejmować, przejąć - to take over; to intercept; to adopt (habit); to overcome
przejmować się, przejąć się - to be worried, to be concerned
"prze" (in front of, before)

przyjmowac, przyjąć - to accept, to admit, to receive
"przy-" ("at, near, close to, by")

ujmować, ująć - to seize; to grasp, to conceive; to formulate; to lessen
"u-" (can mean "off" or "on")

wyjmować, wyjąć - to extract, to take out, to pull out
Clearly this is "wy-" ("out")

wynajmować, wynająć - to rent (e.g. an apartment)
"wy-" ("out") and "na-" ("on, in") are my guesses here

zajmować, zająć - to occupy, to capture, to take up, to take (time)
zajmować się, zająć się - to deal with
"za-" ("behind")

zdejmować, zdjąć - to take off, to take down
This is a difficult one.  Is the prefix "zde-"? Or a combination of "z-" ("with, down") and "de" or "do" ("toward")?

A good deal of what I am writing about these prefixes is pure conjecture.  I don't know if some of these verbs have two-part prefixes or if the second part is just part of the verb stem.  I am trying to figure out patterns and logic that will help to delineate these verbs by their various compound meanings.

These verbs conjugate in the same way.  If you look at the example of obejmować/objąć above, you can extrapolate that pattern to all the rest.  Just put in everything before the -jmować or -jąć, and then use the same pattern for the rest.

For example, for zajmować/zająć:
zajmuję zajmujesz, zajmę zajmiesz, zajmuj, zajmij

Maybe some Polish etymologists can expand on my theories of word formation here.