How to handle "I'd say" when turning into reported speech

He said, "I'd say a lot depends on the student."

When reported: He said he would say that a lot depended on the student. Old style : He said he would have said that a lot depended on the student.

'Would + verb' either stays the same (if it is a more general statement), or can, but does not need to, change into 'would have + past participle' (if we are hypothesising).

'I would buy it if I had the money,’ he said. -> He said he would buy it if he had the money.

‘I’ll help you if you need a volunteer’ / ‘I’d help you if you needed a volunteer.’ -> He said he would have helped us if we’d needed a volunteer.

See here: https://dictionary.cambridge.org/pl/grammar/british-grammar/reported-speech-indirect-speech

However, I think best option would be to omit 'I'd say' to avoid repeating 'said/say'. When reporting statements it is advised to follow the meaning of a verb than its form. Again, see the link above:

She said, ‘You must pay by 30th April.’ -> She said we had to pay by 30th April.

‘It must be awful to live in such a noisy place,’ she said. -> She said it must be awful to live in such a noisy place.

So my choice would be:

'He said that (in his opinion) a lot depends/depended on the student.'