limited funding, in and around 1-2k to furnish an insert]
In getting a warmer house, this may be more cost effective than the current (less expensive) setup, even if you could manage to improve airflow from the basement... less wood used and less time invested for more effective heat. But what is the current flue setup? Don't neglect to add in the potential cost of an insulated liner if you currently have an oversized tile flue in an exterior chimney.