I have and had the same problem. I find it very strange that no one has approached the city about requiring taxis to have on-board solutions for children and infants.
So two things for you. What I did with my child. And, what I am thinking about doing to solve this city-wide problem.
What I did: Initially I did use the Bjorn and a seat belt. Just be sure that you strap the seat belt between you and the baby - the baby needs to be on the outside of the tension. Still, it made me very nervous and scared out of my mind. Now we plan ahead for all trips and avoid taxis when I am on my own and don't have help carrying the car seat.
What I'd like to do: I would like to start by approaching my city council member to start a campaign to require some sort of child restraint solution. If anyone has ideas, information or a desire to join the effort. Please contact me at this site. Thanks.
Good luck.