Solutions for Hypertrophic Eye Muscle Bulge?

There are no solutions that dissolve muscle without damage to the very delicate surrounding tissues.
From your picture, it appears that you are too young to undergo surgery and that these bulges are actually normal in young patients, in my opinion. In older patients who have had previous blepharoplasty by an aggressive subciliary approach, we actually often build a slight muscle roll when we reconstruct the lower eyelid, in conjunction with a superficial cheeklift. The atrophic, overly flattened, contourless lower eyelid look is definitely out!
For older patients or patients with a more severe problem, orbicularis muscle tailoring can be performed (usually in conjunction with a subciliary cheeklift) but it requires an incision along the lower eyelid. This would be an unacceptable sacrifice for a young patient with no existing scars. We have many patients who underwent cheeklift and muscle tailoring surgery on our website and in publications.
Botox to the lower eyelid muscle roll would theoretically work as well, but often the results are accompanied by slight artifact, so not beneficial to the patient.
Filler such as Restylane or Prevelle is a nice option if the problem is bothersome enough; this can reduce the appearance of lower eyelid muscle hypertrophy.

A blepharoplasty is not going to help with eye muscle bulge on the lower lids. The goal of a lower blepharoplasty is to remove herniated fat in the lower lids and remove a small strip of skin as a pinch technique right at the lower lash line. Lower eyelid blepharoplasty is not done to improve muscle hypertrophy.

Dear RKris
Does the fullness get better with slight squinting of the eyelids? is the fullness there all of the time or does it come and go? Do you ever see this in the right side?
There are many approaches to softening the appearance of the 'muscle'. As you can see above - there is no one opinion. Botox is an easy solution however it may result in the lower lid dropping a small amount. if you try this- it is reversible thus if you do not like it it will wear off.
Filling the hollows may help disguise this- using fat grafting or filler injections.
Some may advocate removing a small amount of muscle.
With the surgical procedures- a caution- the shape of your lower lid - it should be supported with a canthal support suture (the tendon of the lower lid) so that the lower eyelid does not drop down.
With Warm Regards,
Trevor M Born MD