this is what the IRS says are factors to consider. no one factor is determinative
https://www.irs.gov/taxtopics/tc762
or file complete and file form SS-8 with the iRS
https://www.irs.gov/pub/irs-pdf/fss8.pdf
how fast the IRS will respond to filing the ss-8 is unknown
ss-8 instructions
https://www.irs.gov/pub/irs-pdf/iss8.pdf
note that as an employee none of your "business" expenses are deductible.
you could not have signed a w-2 form because the form does not have and does not require a signature
more likely a w-4 but signing that form is not determinative.
your other option is to contact the agency and ask them to correct the 1099 (void it) and issue you a w-2. they may have the right to demand you return the portion that would have been withheld for fica and medicare taxes 7.65%. you could also mention you'll be filing form SS-8 with the IRS to make the determination if they say no.
