Link, it is like you are describing MY chest! I was between D and DD by 12 months and folks around here would not believe me.
And yes. Large, conical boobs do NOT work well with virtually any bra (sports bras were the comfort option for me for a good stretch). Now that they are finally filling out, bra cups can start doing what they were made to do... but yup, you can tell they aren't quite the right shape still. Bras are uncomfortable in general, but the discomfort from having large, still growing boobs is like the discomfort of being a square peg wedged into a round hole. And the discomfort seems to come from the cups, not the straps.
The larger my boobs get, and the more they fill out, the more comfortable bras become. But bras are very much a utilitarian and pragmatic thing for folks above a C. Girls new to HRT keep saying how they want big boobs and I keep thinking, "Oh honey, they are GREAT in theory, but a C cup allows you all the fun of larger boobs, while having WAY more options to holster them and move around."