If you can go to jail (and be deported in 24 hours) if caught working (or making income) in Belize while here on a tourist visa (or extended tourist visas) it is bit more than operating int "spirit of the law". It is a just illegal as using drugs in your own home or driving while intoxicated.
Until a law is written that states, "Telecommuters are exempt from paying any income taxes while living and working in Belize and can stay as long as they went", unfortunately these types of workers will need to follow the rules like everyone else, if they want to be law abiding citizens regardless of their interpretation of the law.
The other option is to use offshore legislation and follow the proper procedures that were deigned for these "offshore" services, not doing business onshore (with Belizean people or companies). They have thought of this.
Regardless, proper immigration status is required. You can even get a self employed work permit, should be really easy, and pay yourself a salary under $BZ400 a week, tax free. Now you are legal and on the record.