I’ll open this response by saying that I haven’t done an asymmetrical corset through to completion yet, so these are simply some observations and ideas that may help :-)
I think that essentially, there are two routes to corseting an asymmetrical body: fitting and flat pattern drafting. They’re heavily tied up with one another of course, but one approach may suit you better than the other.
Option 1- Through fitting. Draft a symmetrical full pattern. Make an un-boned or lightly boned toile (don’t bone the seams) and have someone there to help take fitting notes and make alterations to the toile whilst you’re wearing it. Leave the seams unfinished (give yourself about an inch or more of seam allowance) and to the outside of the corset so that you can unpick and pin/baste where necessary to get the lines correct. I might even draw any new stitching lines directly onto the toile.
Once you have let out or taken in the seams where necessary (and also marked where the top and bottom edges need to fall), remove the toile, unpick, and transfer the changes onto each side of your flat pattern. As this toile wasn’t properly boned, I would then do a new toile based on the altered pattern, fully boned with the appropriate seam finishes, so that you can confirm the changes you have made.
Option 2- Through drafting. Draft an asymmetrical full pattern, based upon extensive measurements and observations of your body. For this, you would need to take all the usual measurements, but then break them down further. So for example, along with “hip” and “front hip”, you would also want “left front hip” and “right front hip”, which would be taken from the centre-front line of your torso, out to your side seam. The same is true for the vertical measurements, eg: “waist to high hip, left” and “waist to high hip, right”. You would need assistance taking the measurements, and need to ensure your posture is as relaxed and normal as possible. You then use the measurements to create a pattern as normal, but with left and right drafted separately. Again, a toile to check fit and shaping would be a good idea!
Do also note that each change may have a knock-on effect. For example, it sounds as though you may need an inch or so extra space over the left hip to account for that roundness you mention, and that you may also need to cut down the left underarm slightly. But what could happen, is that once the extra fullness is given to that hip, the corset is no longer being thrust upwards by it. Therefore, the left underarm might now sit comfortably, without any alteration required. This is why I may be tempted to go with option 1, so that you can make quite immediate changes and see the effect they have, whilst the toile is on your body.
I’m sure there are many more (and probably faster and more sensible!) ways of patterning for asymmetry, so do continue experimenting and researching. Best of luck :-)