Since your profile says you live in Kiel, Germany I could offer to replace the socket against one from a donor board. You could also buy a new one and send it along with the board.
However it'd have to be a regular through hole socket (don't think there are any others) and it would probably take me a bit to unsolder 740 pins and solder 370 back so you shouldn't be in a hurry with using that board. 😉
Only got that one reply inquiring about the method and then nothing more. No PM either. I haven't got as much time right now so I can't offer this help anymore.

Doornkaat wrote:

it would probably take me a bit to unsolder 740 pins

But S370 has exactly 370 pins. I have to agree with Doornkaat, socket change is the only reliable way to restore retention mechanism. Doornkaat, are you planning to lift the socket's base using force and then desolder each pin one by one?

SSTV2 wrote:

Doornkaat wrote:

it would probably take me a bit to unsolder 740 pins

But S370 has exactly 370 pins. I have to agree with Doornkaat, socket change is the only reliable way to restore retention mechanism. Doornkaat, are you planning to lift the socket's base using force and then desolder each pin one by one?

Unsolder 370 pins from damaged board + unsolder 370 pins from donor board = unsolder 740 pins 😉
Plus, re-solder 370 pins on damaged board. 1110 solder points in total. This is something that you probably won't do one by one with a soldering iron, but rather with a hot air gun. I am not too bad with the soldering iron myself, but this is way beyond my skills. Always wanted to learn hot air soldering, but this isn't exactly something to start practicing with.
@doornkat: What would be your approach with this? Have you done similar repairs before? And where are you located?

In the meantime I found that there was a thread on the same topic just a few weeks ago, don't know how I missed that in the first place: Socket 370 Zif repair ?

Edit:
Also, I found this video: https://www.youtube.com/watch?v=rgGTo91SOq8
Looks rather brutal to me, so I wouldn't do that to the board that is to be rescued, but for the donor board, why not.

gex85 wrote:

Unsolder 370 pins from damaged board + unsolder 370 pins from donor board = unsolder 740 pins 😉

Exactemundo! 😉

SSTV2 wrote:

Doornkaat, are you planning to lift the socket's base using force and then desolder each pin one by one?

gex85 wrote:

@doornkat: What would be your approach with this? Have you done similar repairs before? And where are you located?

I actually use a heated desoldering gun and soldering iron on every single pin. The size of the socket requires a lot of heat/airflow with a hot air station and without pre heating the whole motherboard the temperature difference / expansion from heating such a large area would put a lot of stress on the PCB. It would be nice to have that kind of equipment but I don't, so it's one by one. This is why I said it might take some time. I probably won't do the whole thing in one session. 🤣
I haven't done Socket 370 as of yet, but 486 ZIF conversions, RAM, AGP and ISA slots. Also EPROM sockets and larger through hole ICs. So far all successful. Still I'm not doing this professionally or as a business and I can not offer any warranty.
I'm located in Germany.

gex85 wrote:

Also, I found this video: https://www.youtube.com/watch?v=rgGTo91SOq8
Looks rather brutal to me, so I wouldn't do that to the board that is to be rescued, but for the donor board, why not.

So this is how those refurbished sockets with bent pins inside end up on ebay...

My tools, used for desoldering sockets or slots of any type, consist of only 2 things: a heat pad and a heat gun. I'd recommend only this type of socket desolder in your case, it's easy, fast and risk-free.

Doornkaat wrote:

It would be nice to have that kind of equipment but I don't, so it's one by one.

TORTURE 😵

I think that I would just do the super glue and clipped plastic end of zip tie trick.

Or some other kind of plastic, I've seen people use super glue mixed with baking powder or cornstarch to build up the plastic where the tabs are broken and then gently file down the excess.

If not carefully it isn't too ugly, and once the heatsink is on there no one will ever see it.

I think i watched a YouTube video on it as well.