Does FT3+ offer an SVG export? If not, does it have a documented save format that I could post-process?
It's a little twitchy, which is why it's not available by default. Use File>>Save Campaign Cartographer File, then hold down the Shift key while clicking Create (to make a new thing) or clicking Edit (to change an existing one). Select "Scalable Vector Graphics (SVG)" instead of "Campaign Cartographer 3" and you'll be able to use that export setting to generate SVG contours instead of CC3 contours. I don't guarantee that it works correctly or that you'll be able to use it, but it was there and sort of worked (except for really bad scaling) before.