If you have an EAP, I would signpost to them to see if they can help, if not get Occupational Health involved. Maybe even suggest they take some annual leave to reset themselves. In any event I suspect they will go sick in the near future.

In all seriousness, though, there are several ways to approach this:

1. Coaching

It sounds like you're already doing this, but I don't know if you're taking a coaching approach, in which the ability to stop working is framed as an opportunity for professional learning and development rather than just being an issues of (mental) health. Depending on the approach you've taken so far, the answer might be "the same thing, but different".

2. Discipline

You mention that their behaviour also manifests in the form of getting involved outside the remit of their project. This may be a disciplinary issue and this might be a way to get through to them that their behaviour isn't just bad for them, but bad for the business. Their "perfectionism" is, in fact, creating flaws and errors that would be avoided if they could calm down.

3. Natural wastage

This is an uncompassionate approach and not one I'd recommend, but it can be appropriate depending on the employee. Let them break. Some children have to learn the stove is hot by touching it and some people cannot understand the potential consequences of their actions until they arrive at them. Of course, have a safety net ready, but in some cases this is the only wake-up call an employee will hear.

In addition to the helpful posts above which I wont repeat - a more radical solution might be to deny them access to your IT systems outside certain hours. May not help their stress levels but its a very clear sign you are serious

I know coaching has been mentioned above but how about sending them on a time management course, sometimes that's all its down to. It seems so simple but I've come across a few situations lately, where stress is down to poor prioritisation. If you think that would escalate the situation do it as a group thing or send more than just one person on it.

Slightly different angle, I had an employee who everyone said "oh X is so lovely" "bless them" and always had this apologetic, self-blaming, and unable-to-say-no attitude.  They would very often stay until 8pm, 10pm to "perfect the work" or "to do this one favour". The reality was that they were just slow and incompetent, and their peer colleagues were picking up A LOT of their slack. When the peer colleagues gave notice to move on at the similar time, this employee couldn't bear the stress and fear of being the "most experienced" peer to the new replacements, they quit without having the next job waiting.

Welcome to the Community, Anna. I like the suggestion above of a time management course. Really this ought to be something a good line manager should routinely deal with.