What size is that HS? S7 coolers don't need to be big. Mine is quite tiny to be honest.

You broke the side top\bottom prongs too?
If they are still there you can use a Socket A clip that has the 3 holes most of these are long enough for Sk7. The Upper and Lower of each side will take the pressure. I had to do this with my Packard bell c110, as it aged the OEM clip slowly cut through the prong leaving it with no standard way to hold the sink. So I simply installed a sockat A cooler a 3-prong socket A clip which grabed the remaining top left and bottom right prongs.

Just make sure the clip doesn't feel like its gonna take 100g's of force to secure the clip.
Some socket 370\A clips are just not long enough or just long enough they apply far to much pressure to the socket prongs.

If that would not of worked I would of resorted to using one of those heat-pipe tower style chipset coolers, and would thermal epoxied it onto the cpu 🤣 .
Since the base isn't huge on those they leave enough clearance for the socket leaver.

I don't know a current source for bare sockets. A few years ago I actually saw somebody on eBay liquidating large numbers of them. They had some listings for hundreds of unused CPU sockets from some manufacturer. But desoldering an entire CPU socket seems like it would be quite a project. Maybe with good equipment it wouldn't be as bad as it sounds. I know I could never do it.
If you are able to do this, then of course another motherboard would be a potential donor.

I've had this problem a few times with socket 370. The design of socket-7 seems to be pretty much the same.
The idea of a 3 prong clip seems like the best solution. I don't know where to get a clip that is actually suitable for this though. I've never found a socket-A clip that wasn't absurdly tight on socket-370 - I assume socket-7 would have the same problem. If soft 3 prong clips are really out there though, then that would be a good fix.

If the board can lay flat, then securing the heatsink becomes a lot less critical.
You could try epoxying the broken plastic but I agree it might not hold. If you try that, only use a slow setting 2 part epoxy like JB Weld or similar. Even that is a longshot, but if it sets strong enough and you use a very soft clip from now on, maybe it would make it. I doubt anything fast setting or single part would have any chance.

If there are smooth edges it might help to rough them up. Any sort of splint you can come up with might help to reinforce, but I have no idea how you'd position that in this situation. I was able to repair a stressed structural plastic piece on an mPGA478 heatsink using JB Weld, and it has held for years, but it has a large splint helping it out. Using only the original mating surface, you might not have enough area to make it strong enough. I have no idea how you'd reinforce a socket-7 retaining hook.

Last resort is to use thermal epoxy to permanently attach a heatsink to the cpu. You could offset the heatsink such that you still have access to the ZIF lever. In that case you're relying on the pins of the socket to hold the torque of the heatsink, which is probably no problem for any typical heatsink and a stationary PC.

The offset retaining hooks on socket-7/370 always seemed really strange to me. I don't know what they were trying to do with those. 3 hooks on each side would be nice, but 2 at opposite corners is just weird. The only clip I've seen that actually uses them was from a Compaq Deskpro, and I ended up breaking a socket with it because it was so awkward to use.