grammaticality - Is it "our work and that of others have demonstrated" or "our work and that of others has demonstrated"?

In your example sentence you have no choice but to use the singular.

For the avoidance of doubt, the plurality or otherwise of 'has/have' has nothing to do with the adjacent 'others'. The verb follows the plurality of the subject, which is 'our work and that of others'. The question is: is that a singular or a plural noun phrase?

Not many speakers would argue that 'our work' + '[work] of others' adds up to two 'works'. Other than in the specialised usage of 'book', 'work' is a mass noun. It doesn't get pluralised. 'You do some work, I do some work; together we do some work' (as opposed to 'I write a work of literature, you write a work of literature, together we write some works of literature'). In the sense of 'work' as 'labour', the subject is singular and the verb should be 'has'.

If the sentence had instead been 'My subscription and that of my parents has/have expired', there would have been more room for debate. I would have gone for the plural, in that the subject is the total of two subscriptions. However, the singular doesn't sound terrible either, because you could rephrase the sentence as 'My subscription has expired, and so has that of my parents.'