In your original logo the little rings are purely decorative, but in the Amharic I think they may be confusing to readers, since Amharic readers are used to treating most end-of-stroke details as meaningful. So my suggestion is to utilise this feature of the script and in the Amharic version use the rings systematically as 'flag' replacements. I believe you can simplify the mid-stroke arms as you have done, but that you should maintain the top and bottom flag patterns, using the rings. I would revise the first syllable form to maintain the connection between the left and right sides. I think you could safely double the crossbar of the middle syllable to echo your treatment of the original logo. So, I suggest something like this:

... and check with a native. I'll send one over. :-)

hhp

This web page might introduce one to the sensitivities present in the subject at hand...

Hi Harnt , Hope all is well. As John has pointed rightly, In Amharic end of strokes are meaningful .
Whenever you think of Amharic script you have to think of writing sequences(or stroke). It is because
We have 34 basic characters and they are modified in to six variations. In your case the word comes from two basic characters which looks like t and H the red and the blue are diacritical marks which change the basic sounds . I have also circled the 3 characters you used in your logo. That is why it is important following the structure of each letter not to confuse them.
When you write each character you have to follow a rule. The rule is to finish from left to the right . Traditionally going back is not allowed (Please see the image below ). For example the letter a has to be written only in this order.(Finishing from left )

When you want to modify a script like you are trying to do, You have to think of the skeleton of each characters. John’s suggestions maintaining the flag patterns is important, however in this case putting the rings above, below or at the center of the Joints(Like I did) it will increase legibility. This is Where thinking of the skeleton of the characters comes handy, for example on the 3rd character . The bottom is not horizontal it is diagonal.
To answer your questions:
How specific those strokes and symbols need to be? As long as you maintain the skeleton of each glyph it does not have to be specific. What you started is good and looks different from what we have seen.
Doubling the cross bar or making it wider or narrower will make it only beautiful.
Is there any guide somewhere? So far I don’t know any guide. I am working on a book. God knows when I am going to finish it. Whatever questions you have you can e-mail me.
To demonstrate what I am talking about here is a quick example ..

@ John I have not talked to you for so long how are ? Will e-mail
Aleme

And people talk about the demise of Typophile. Where else can you find this level of help and insight?

[interesting]

Hello, Aleme! I wondered about that third character, and whether it was a mistake to make the bottom horizontal. Thanks for the clarification.

Thanks for your suggestions, folks. And thanks for the helpful lecture, Aleme! I shall make some amends.

OK, did some tweaking. Not sure about the ring in the last character, but as John rightly pointed out, it's purely decorative. I'd imagine, Ethiopians would see it the same way (as long as the skeleton is right)? It also nicely counter-balances the diacritical mark on the first letter. Three rings, as suggested above, seemed too much in a short word. Again, I'd appreciate pointing out any mistakes. Thanks.

Hi! I would say it is beautiful !! As a graphic object it is beautiful . Having different width make it more lively and matches the Latin characters. For a native reader it is Legible and look nice . Judging by the meaning of the word I am just guessing this might be for music album or book cover . I think it works well . John has very good feeling and knowledge of Ethiopic. Yes it is purely decorative but the way it is done now is good. To make it real perfect (For my eyes) the horizontal bars on the last two characters has to be a little bit up (As you see below )

Thanks Aleme. It's actually an Ethiopian food delivery service :)