You don't have to change the address for payroll purposes. Your permanent home is Florida. The other states are temporary stays.
Since your company is based in Connecticut your wages would be subject to CT income tax for the six weeks you work there.
The other states except New Mexico tax telecommuters by resident state, i.e. nonresident telecommuters are not subject to tax in Massachusetts and New York. New Mexico has not issued any guidance, but you are probably not subject to NM tax.
You can make an estimated payment to CT or you can wait until next year to pay any tax due on your nonresident income tax return.
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