Here are 3 solutions to this issue that each have their own upsides and downsides.
1. Use different tag words and normal quotes
Usual tag words for dialog are things like "said", "whispered", "shouted". For signed language you can use "signed" and possibly throw in adjectives for other variants than the 'default' (signed energetically, signed quickly, signed slowly, signed surreptitiously).
Ex:
"Are you sure this is a good idea?" he asked her.
"I've never been more sure of anything in my life," she signed to him.
I've never been less sure of anything in my life, she secretly thought.
The upside is that this explicitly says how the information is being communicated. The downside is it only works so long as every line of dialogue is tagged appropriately - getting repetitive.
2. Use different quoting characters
Use quote characters from other languages for signed statements. Things like the double guillemets « like this » or the single guillemets ‹ like this ›. While not the standard in English they are simple enough to understand and would provide a different appearance to the signed text.
Ex:
"Are you sure this is a good idea?" he asked her.
« I've never been more sure of anything in my life, » she told him.
I've never been less sure of anything in my life, she secretly thought.
Alternative quoting characters from English-related text can be borrowed from programming where there are three main types of quotes used. The usual double quotes "like this", the single quotes 'using apostrophes' and the angle/backtick quotes like this
. Single quotes obviously can cause confusion with apostrophes so might not be the best idea
Ex:
"Are you sure this is a good idea?" he asked her.
`I've never been more sure of anything in my life,` she told him.
I've never been less sure of anything in my life, she secretly thought.
The upside is that this marks the information as being delivered differently than the spoken dialogue. The downsides are that it uses characters that English speakers/readers are not as familiar with for the quotes, and it doesn't explicitly say how the delivery is different.
3. Italicized quoted text
This is much like the example you provided except that the only text in italics is also in the quotes. Internal monologues would be in plain regular text.
Ex:
"Are you sure this is a good idea?" he asked her.
"I've never been more sure of anything in my life," she told him.
I've never been less sure of anything in my life, she secretly thought.
The upside is that this marks the information as being delivered differently than the spoken dialogue. The downsides are it means you cannot use italics for other forms of emphasis (or language differentiation), and it doesn't explicitly say how the delivery is different.
Conclusion
I would say a combination of the first option and one of the other options is best.