I'm also a bit curious about optical stores which fill scripts on lenses, general pricing, and their turnaround time.

As you mentioned, Masunaga has a few flagship stores in large cities https://www.masunaga1905.com/en. They also stock Kazuo Kawasaki https://www.masunaga1905.com/kazuokawasaki/store which has a non-brand-owned retailer list. You might want to email https://www.eyewearnation.com/ in USA to see if they have access to Masunaga. I get my Kawasaki frames there as my optician no longer has a contract with the Kawasaki supplier and invoice my vision insurance & FSA for reimbursement. They're also priced a bit better than what my optician offered. I have my optician fill the prescription lenses and they specifically use a Hoya lab for this particular order (single vision polished rimless drilled trivex with AR coating). They do the insurance submission paperwork for what's covered and I submit the rest to my FSA.

I also sometimes have Zoff/Jins frames (re)filled at home after trying their in-store labs. I need the axis tolerance closer than they allow for but like the lightweight and flexible ultem frames. They have a few sunglass frames I like but didn't offer polarized prescription lenses and they're also larger lenses, so I have those filled locally as I've found vertical height is likely to be off if they don't mark the centers for the lab. I've also taken a pair back to the optician to refill as the coating developed crazing (warranty covered it and I don't leave them in the car now). Some family and friends with trickier prescriptions also benefit from the local optician as it can take a few rounds of fills before things are exactly right. I know the lab(s) has also sent improperly filled glasses which my local optician has redone before they call me to let me know the didn't pass their quality check. These are reputable labs. I probably have slightly picky eyes despite lower prescription and trickier to fill frame preferences.

I'd try Zenni's Ultem line with trivex but nose bridge challenges and the JP brands have wires to allow temples to be fitted. Asian fit styles work better for me. I haven't gone to the local Gentle Monster S. Korean store but there seem to be some stylish options there, too.