I am not sure what your definition of stratosphere is but a good Imperial convertibles built in the 1964 through 1968 period can be purchased from $8000 to $12,000 for condition #3 models, which are solid servicable (running) models in good physical condition but not trophy winners. Older models, 1957 - 1963 in #3 condition will cost more. A good source of information on the cost/availability of these cars is e-bay as in the past year many Imperial converibles have been auctioned on ebay ( I bought one).
Don Dickinson
Prospect, KY
1955 Imperial Newport, Canyon Tan and Desert Sand
1967 Imperial Custom Convertible, Ivory and Burgundy