Standard CBC designs where you've shown respondents discrete price points (e.g. $5, $6, $7, $8, and $9) for SKU A will still allow you to simulate any possible price between $5 and $9, even if you don't use "summed price". Our simulators support interpolation between points shown to respondents in the study. Straight-line interpolation is applied, with straightline between the two nearest estimated price points.
So, if this is the main goal, you can save yourself a world of effort by just doing CBC in the standard way (not continuous price) but using the interpolation capability within our simulators.