Help identifying portrait large bronze plaque circa 1875 please

Sorry if the answer is obvious, but all those guys with the post Civil War beards look alike to me.
My guess is Rutherford B. Hayes, but also looks like Garfield to me.
24 inch bronze plaque. Came from a New Hampshire shop who bought it around 1980 from a guy who claimed his dad was a construction worker when the old Boston Copley Square Main Post Office [(built in the 1870s ](https://www.historicnewengland.org/explore/collections-access/capobject/?refd=PC001.01.TMP.094 "(built in the 1870s
was demolished in the 1920's, and that it came off the PO wall, bought it for scrap as a souvenir.
New Hampshire shop had it on the wall, thus the modern fixtures, easily removed.
Thanks for you time!
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No idea about the plaque, but, the screws on the back are not from 1875.
If it was in a Post Office facility, might have been a portrait plaque of the Postmaster General....?
Agree that the screws and attachment are not old --- maybe mid-20th century.
Excellent idea, thank you, However I had checked the Smithsonian Portrait Gallery of PG's and none of the post-1875 PG's have that spectacular beard length or long hair. I am assuming that if not a President, it has to be someone who was in office after construction was completed.
Nice old bronze plaque... have you tried to remove those screws? Could be something in between the two pieces.... Maybe even identification of the image. Cheers, RickO
Copley Square pics, then and now.
http://lostnewengland.com/tag/copley-square/page/3/
I am inclined to think it is Rutherford B. Hayes.
The mounting was amateurishly repaired.
RB Hayes as president fits with the timeline of the Post Office story.
As suggested, it could also be someone local - I would check to see if that PO had a formal name (if it was named after someone). Of if it looks like Copley himself. There are a couple old libraries and historical societies in Boston that might be able to help ID the portrait.
Interesting construction if it is two pieces - what are those brass screws holding together?
My guess would be Rutherford B. Hays. Here is a campaign piece from his 1876 run for the presidency. Hays pieces are surprisingly scarce. Wheeler was was his running mate.
I suspect it is an idealized portrait of James Garfield. Probably done as a memorial plaque shortly after his death. It could also be Hayes, also idealized. The idealization of the portrait, if done, makes it difficult to be sure.
@291fifth I agree with what you are saying.
The OP’s pic looks like a person that is experiencing some type of pain, physical and/or mental. IMO
@Que_sai_je Have you been able to disassemble and look at the back of the bust?
Thanks everyone for all the input.
1. Don't trust myself to do so w/o damaging it further. It does seem to me that it was probably originally set into a recessed custom depression in a wall. Don't know what would be on the inside, usually cast uniface have no markings on back.
2. Looking at the the Hayes/Wheeler token above, I agree it is probably Hayes. Hairstyle and severity matches, also perhaps a portrait of him as an older man. A contemporary commercial sculptor would have had recent photos.
3. Now that I think of it, no reason to me why this needs to have been a one-off: I wouldn't be surprised if portrait plaques of the President had been used in public buildings generally, Maybe someone here has seen another?
Here's a portrait by George T. Morgan:

https://npg.si.edu/object/npg_NPG.76.108
Pacific Northwest Numismatic Association
Morgan's portrait was much admired at the time.
My new "theory" is that the building was secretly used to make cough drops. Originally, there were bronze portraits of all four Smith Brothers on the factory wall -- to inspire the workers! Then, one sad day, a Smith brother discovered he was only a step-brother and his real name was Jones. He immediately went out, got a shave and a crew-cut, then turned the others in to the District Attorney for the reward offered for making unauthorized cough drops under a false name.
The "Lone Jones" company then went out selling cocaine to overworked child laborers, and milk adulterated with plaster of paris.
Thanks @carabonnair!
@Que_sai_je Both pics for comparison.