If you add 'but her name' then the sentence is easier to understand.
In the original, there is no comma, and the sentence continues further.
The character Rajkumar is talking to someone, a little girl I think, called Dolly, giving her a jewelled box.
She appears to be poor or a beggar, he gives her the valuable thing, then he is repeatedly saying her name 'Dolly, Dolly, Dolly!'
Then it says 'he could think of nothing else to say worth saying'
So it means, he is saying her value, in her name. He shouts it louder and louder 'until a tiny smile creeps on her face'.
So he states her name, as a way of connecting her to her own value.
And in that moment, as he does that, it says: 'he could think of nothing else worth saying'
It's as if he has made a deep connection with the girl, in just that moment - they are in a kind of time bubble, as he recognises who she is - and endeavours to wake her up to that, by saying her name.
So her name becomes precious in that moment - her name becomes 'the only thing' and saying anything other than just her name, would not have the same effect.
If you add 'but her name' then the sentence is easier to understand:
'He could think of nothing else to say or as much worth saying - but her name.' Meaning 'but only' her name. Only that will do.
There is an inferred 'but her name' in the original - although it doesn't say that, that is what it means.
The full sentence goes:
- 'He could think of nothing else to say or as much worth saying, so he said the name again, louder and louder, until he was shouting. "Dolly. Dolly."
And I suggest it could be more easily understood if you think of it as inferring 'but her name' like this:
- 'He could think of nothing else to say or as much worth saying but her name, so he said the name again, louder and louder, until he was shouting. "Dolly. Dolly."
This is by Amitav Ghosh by the way, so it is not archaic, but without the 'but...' and without the context, it certainly sounds archaic!
So, coming back to your question of how to use the phrase, I think if you add an 'as..., but... or except...' on the end, then you will be able to. For example:
- he could think of nothing else to say worth saying except - sorry
- he could think of nothing else to say worth saying but 'I love you'
- he could think of nothing else to say worth saying as she left