Remember, if you create summed pricing without the random shock to the sum total each time, you will correlate the features with the prices shown, and you will not be able to estimate a price slope (price sensitivity). Sounds like you're understanding that, though.
Also, if you do the same thing through conditional pricing without having a separate price attribute that varies the prices, say, -20%, +0%, +20%, you won't be able to estimate price sensitivity.
You understand correctly that conditional pricing takes the different premiums or discounts for, say, premium brands and discount brands and then varies those by, say, -30%, +0%, and +30% (if you had 3 levels for the price attribute).
But, I'd be cautious about trying to make conditional pricing based on more than one attribute. If there are significant interaction effects in the utility parameters, then you'll not be able to untangle them only with main effects + first order interactions. That said, many researchers still do use conditional pricing based on more than just one other attribute. Just make sure the conditional pricing elements are additive in a logical formula rather than haphazard. If the conditional pricing elements are combined haphazard, you'll confound the utilities with the experimental design.
Summed pricing is possible in CBC, but only via a "power trick". I just did one last year like this. It involves exporting the CBC design file (assuming
a standard price attribute with, say, 7 to 10 levels) to the .CSV file, then modifying that file. It's somewhat involved, but it involves calculating the summed price plus a random shock for each concept in the design. Then, it involves mapping those summed prices into the 7 or 10 discrete levels for price...assigning those concept prices discretely into the nearest 7 to 10 discrete price buckets. So, essentially, you're creating a summed pricing design where you are rounding the end prices to 7 or 10 discrete price values. Once you've done this, you import the design and test the design efficiency again. In the model building phase, you can estimate price as either the standard part-worth functional form or also as a linear form.
The number of levels effect is not as big of a deal as the papers from the 1980s suggested. Those articles from the 1980s pointed out the problem if you had 2 levels for the full range of a quantitative attribute rather than 4 levels (but both cases covering the same range). It turns out that if you are comparing 3 levels to 6 levels; or 4 levels to 8 levels, you just don't see nearly the same number of levels effect as when comparing 2 to 4 levels. So, it seems mostly a corner case involving such a low number of levels for a quantitative attribute (2) that it is unrealistic to real world practice.