Continuing work for a non-US employer during J2 visa

Below is the specific context for my question:

• Already working for a non-US employer, but would like to accompany spouse who is visiting US on a J1 visa for a fixed duration (6-9 months). The duration will NOT be longer than this for sure.

• My current employment is a permanent work-from-home position for a non-US employer.

• To be able to travel to the US on J2 visa, can I go on unpaid leave from my current non-US employer, without terminating the job? (of course assuming the employer is supportive of this)

• Once I apply and receive the EAD in the US, can I then resume working for my current non-US employer?

• If the above seems legally fine, what documentation should be provided at the time of the J2 visa interview? (E.g. would a letter from the employer confirming the unpaid leave until suitable employment authorization be sufficient?)

We are unable to find a resolution to this issue, and would sincerely appreciate your help and advice.
Many thanks in advance.