A Residente Temporal (temporary residency visa) does not automatically give the right to work in Mexico - you need a work permit endorsement added to the visa.
That said, Mexico allows people to work remotely while living in Mexico, as long as a) you're not taking a Mexican job, and b) all your income is paid into a non-Mexican bank account. This was the advice given to me by the Mexico Consulate when I was granted my RT. I was not given a work permit, but was told it was no problem as my work/pay was remote from outside Mexico.
There are many people who live in Mexico on a tourist permit, renewing the permit every 6 months. Someone I know was advised by the Mexico Consulate that while she didn't meet the financial requirements to obtain residency, she could just continue to renew the tourism permit every 6 months. She did this for 2.5 years without any problems. I am also aware of other people who have been doing this without issue for many many years.
Talk with your local Mexico Consulate, they will likely give you the same information I was given.