grammar - Comma before adverbial participial phrases (reduced adverbial phrases) and participial prepositions

Another tricky comma question that has recently popped up in my line work that I have not been able to resolve to my satisfaction. Apologies it's a bit long, but all parts are related and additional details + references are provided for responders' benefit.

The question comes in 2 parts.

Comma before adverbial participial phrase

Do we put a comma before a participial phrase that follows the main clause when it stands for reduced adverbial phrase (see "NB!" below on why I call these participial phrases reduced adverbial phrases) and is restrictive in meaning, and if yes, why do we use such comma?

Couple of examples:

1. I came to work today(,) wearing my new suit. ("Wearing my new suit" stands for "While wearing my new suit", with full sentence being "I came to work today while wearing my new suit".)

Is the comma necessary before wearing, given the participial phrase is intended to be restrictive in meaning. If the comma is not in the full sentence, it should surely not be in the reduced sentence?

2. She is very lucky(,) being suitable for this job. ("Being suitable for this job" stands for "because of being suitable for this job", with full sentence being "She is very lucky because of being suitable for this job".)

Is the comma necessary before being, given the participial phrase is intended to be restrictive in meaning. If the comma is not in the full sentence, it should surely not be in the reduced sentence?

3. He walks(,) dragging his left feet. (Full sentence: "He walks while dragging his feet".)

"Dragging his feet" restrictive, and no comma in full sentence - so no comma?

4. I escaped(,) using a fire exit. (Full sentence: "I escaped by using a fire exit".)

"Using a fire exit" restrictive, so no comma?

5. Today I came home(,) having only finished half of my workload. (Full sentence: "Today I came home today after having only finished half of my workload".)

"Having only finished half of my workload" is restrictive, specifying the circumstances in which I came home (otherwise with comma it reads "I just came home today"). No comma in full sentence, so no comma in reduced?

Doing the research across various publishers, I see commas are generally dropped in constructions 1-4 (present participle tense), but not in construction (perfect participle tense) 5.

In fact, if you check this link - example 1 and this link - example 5, two identical constructions, one in present tense and the other in perfect tense, has different punctuation (present tense = no comma; perfect tense = comma). Why? Surely, grammatical logic should be the same irrespective of the punctuation?

Same is true for this grammar site, which talks about the subject: no comma before adverbial participial phrase in present tense, but there is one in the in perfect tense (why is this?):

Present:

Tom lost his keys (while) walking through the park. (Tom lost his keys while he was walking through the park.)

She left the room singing happily. (She left the room as she was singing happily.)

Perfect:

Mark knew the town well, having lived there all his life.

Is there a general guideline as to why commas are present or missing? Grammatically, if they modify the verb, just like any adverbial, and are restrictive, comma should be omitted in both present and perfect participial phrases, correct?

NB! I know that traditional grammar says that participial phrases modify adjectives; however, there is plenty of sources that say that they can also modify verbs, including BBC, British Council, CMOS, GMAT.

Couple of more examples:

6. You did well(,) compared to me. (Full sentence: "You did well when compared to me".)

"compared to me" restrictive, and no comma in full sentence - so no comma?

7. This is not a bad day(,) taking into consideration what others suffered. (Full sentence: "This is not a bad day when taking into consideration what others suffered".)

"taking into consideration" restrictive, and no comma in full sentence - so no comma?

Comma before participial prepositional phrase

Similarly, does one need a comma before participial prepositional phrase that follows the main clause if the meaning of the prepositional phrase is restrictive, and if yes, why?

Quick reference on participial prepositions from Gregg Reference Manual, 1oth edition, section 1082 NOTE:

NOTE: A few participles have now become established as prepositions; for example: assuming, concerning, considering, depending, following, given, granted, judging, pending, providing, and regarding. Therefore, when they introduce phrases at the start of a sentence, it is not essential that they refer to the subject of the sentence.

Few examples:

8. This is good result(,) given how other teams performed.
   Given acts as restrictive preposition; restrictive prepositional phrases do not take commas - so no comma?




9. I will stay late(,) assuming you cover me tomorrow.
   Assuming acts as restrictive preposition; restrictive prepositional phrases do not take commas - so no comma?




10. You performed well(,) considering how other people managed.
    
    Considering acts as restrictive preposition; restrictive prepositional phrases do not take commas - so no comma?

Summary

The three main questions are:

a) How to punctuate the above adverbial participial phrases and are there any guidelines? If the participial phrases are restrictive adverbial reduced phrases, can the comma be dropped, just like in the full sentences when subordinator is present?

b) Why when the adverbial participial phrase follows the main clause there is no comma in the present tense, but there is one in perfect tense (based on majority publishers), despite having identical grammatical constructions (albeit different participle tenses)?

c) How are restrictive participial prepositional phrases punctuated? Should they be treated in the same way as non-participial prepositional phrases without the comma?

Is it fair to say that:

1) Adverbial participial phrases act adverbially and thus modify the predicate in their respective main clauses, just like their equivalent full phrases & clauses they stand in for - therefore, requiring no comma as they are restrictive in meaning?

2) Participial prepositions act adverbially and thus modify the predicate in their respective main clauses, just like their more frequently used alternatives (For example, in example 8, "assuming" can be replaced with "provided" or "if", both of which take no comma as the meaning is restrictive. Surely the same applies to "assuming"?

Most style guides, including CMOS, don't give much info on participle phrases; however, Gregg has this section:

Gregg Reference Manual, 10th edition, section 137:

When a participial, infinitive, or prepositional phrase occurs at some point other than the beginning of a sentence (see 1135) or the beginning of a clause (see 1136), commas are omitted or inserted depending on whether the phrase is essential or nonessential