OP's usage was common enough a century or two ago, but today you'd normally only find for being used to mean because in deliberately archaic/poetic contexts...
Lord, help me for I am poor and alone.
My guess is it's impossible to recast OP's exact words into a "simple" sentence (whatever that means), because semantically there are effectively two separate elements...
We forgive our enemies
[So/Therefore, please/you should] forgive me
You can only recast it into more modern English - "We forgive our enemies, so you should forgive me".
As has been pointed out, perhaps what OP actually means is "Forgive me in the same way that we forgive our enemies". Because the sentiment itself has "dated" religious overtones of The Lord's Prayer ("Forgive us our trespasses as we forgive those that trespass against us"), it's not a good example to "modernise". But in general we tend to use like in such constructions today...
"I just wish you could love me like I love you" (where as would be somewhat dated/poetic today).
It's also worth pointing out that as = because could be used in my first example, but my feeling is that in general we tend to avoid using as with either of those senses today. Or if we do, we tend to use other "devices" to make the meaning clearer...
1: "As you said you wouldn't be home until late, I only cooked tea for myself"
2: "I only cooked tea for myself as you said you wouldn't be home until late"
Putting as at the start in #1 makes it "stand out" more, so it's easier to parse/interpret (but probably most speakers would use since or because anyway).
3: "I only cooked tea for myself, just as I usually do on Tuesday nights when you work late"
Including just also helps the usage stand out - again, making it easier to parse (but many speakers today would use like there, even though others may consider such usage "slangy").
The stronger clause of two clauses conjoined with "although" is the main clause, NOT the subordinate clause with "although". So, while both "although" and "but" are used to show contrast, they have opposite meanings in terms of which is the stronger clause. I'm not surprised to find this poor definition in Wordlink and the American Heritage Dictionary. As usual, Merriam Webster gets it right:
definitions: in spite of the fact that : even though
synonyms: albeit, as, howbeit, much as, notwithstanding, though, when, whereas, while, whilst
So your first example about reputation means, "He has a great reputation. Incidentally, not many people know him." Your second example means, "Not many people know him. Incidentally, he has a good reputation among those who do." These are clearly different to each other in emphasis.
To contrast "although" with "but": "He is known to only a few, but his reputation among them is very great" carries roughly the meaning of your first example, but the conjunctions introduce different clauses.
Best Answer
From your linked website:
The two examples are of additional information, meaning that it would be fine to leave out this information, even if it is interesting. Linking with the present participle gives no more or less emphasis than using other kinds of linking.
With all of these, the second part is subordinate information, but all are of (more or less) equal emphasis. You can even put two (or more) in the same sentence: