Would it be possible to lengthen/“masculinize” the lower third of my face? (Photos)

Sliding genioplasty is an extreme surgery that I don’t recommend unless you have functional issues. To fix the cosmetic problem of a weak chin, a chin implant would give you the correction you want. You must find an expert facial plastic surgeon to help you with this. I hope this helps.

Based on these photos I am not sure that your mid and lower face need elongation? It appears that your high hairline is making your upper face visually longer than it is? In-person consultation with some measurements is needed for better evaluation. You may wait to finish with hair restoration before undergoing "face lengthening". If needed, this is best achieved with implants. Good luck.

When considering facial elongation, which largely can only be accomplished by vertical lengthening of the lower jaw, you have to decide whether you just want it done at the chin area only or the entire jawline. If only the chin is needed then an opening wedge vertical lengthening bony genioplasty can be done. But if you want the entire jawline lengthened, the options are to combine the sliding genioplasty with custom made vertical lengthening jaw implants or perform a 'chin wing' osteotomy'. (which is really just a long extended sliding genioplasty. The key decision is the extent of vertical jawline lengthening you desire.

 Hi, I have performed many facial shaping procedures using dermal fillers, silastic facial implants (cheek, chin), liposuction and/or facelifts for over 30 years.  Following my beauty principles, men look chiseled and handsome with angularity in the cheeks, chin and mandibular angles.  From the photos, your beard pretty much blocks the chin and mandibular angles from being evaluated for weakness.  The cheeks do appear flat to concave in the front.  This combines to create an elongated, oval shaped face.  The following procedures would create a more ruggedly handsome face.
Cheek augmentation with cheek implants to add angularity to the cheeks and mid face.  Liposuction can be combined to reduce any excess fat to further shape the cheeks and face.
If the chin is weak, Chin augmentation, using a chin implant, to add projection to the chin creating harmony and balance to the lower face.  I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut bone segments).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.  
Augmentation of the mandibular angles using a dermal filler (jaw implants have too many unwanted side effects IMHO) to add volume, angularity and flare to the jaw line.
Hope this helps.