Can Invisalign correct my overjet with distalization? (Photos)

Amputating teeth and doing contraction orthodontiics is the last thing you need.  The problem is an underdeveloped maxilla that cannot hold all the teeth without expansion.
Ideally, expansion would have been done when you were young.  As an adult the DNA Appliancee can give you orthopedic growth and turn your narrow "V" shape maxilla into a wide "U" shape.
This will improve yor airway, head position and give better support to soft tissues of your face.Your lower jaw will move forwar into space provided.  The RNA version can accelerate jaw advancement and treat sleep apnea, snoring or morning headaches.

I believe the less treatment needed to solve the  problem the better. Your photos do not show the situation of your lower teeth so I cannot do anything but surmise.  If the lower anteriors are crowded you may be able to combine lower arch expansion, intrusion of the upper incisors and distalization using slight thinning between strategic teeth  ( Called ipr) and accomplish the look and healthy bite you want without any teeth removal or surgery.  Seek a second opinion in person with a qualified invisible orthodontic dentist ( Invisalign & Clear Correct)

It is hard to say for sure with the limited photos you provided,  but I think the best option for you would be to align your upper teeth and then have your lower jaw advanced with surgery,  You have great teeth, great soft tissue contours, but the length of your upper lips is on the short side and any loss of support would collapse your upper lip and make your nose look bigger,   It does not matter whether you take out premolars or 3rd molars, the result will be the same.  Your over bite is because your lower jaw is to short, not because your upper teeth are to far forward.  To check this out how much better moving the lower jaw forward would be, bite together with your lower teeth just in front of your upper teeth, put your lips lightly together,  and take a profile photo.  That would pretty closely approximate your result with moving your jaw forward surgically. If surgery was not an option, you would be better off straightening your incisors and accepting a little more overjet.  If you move your front teeth back, half of the red part of your upper lip would disappear and I think you would be very unhappy.  I know this all sounds invasive and very dramatic.  For context, please read some of my other posts.  I am not against removing teeth for orthodontics (as some are)  and I have posted a lot on this site (kind of a hobby) so you will see that I do not often speak against removal of teeth and usually don't speak in such strong terms.  That said, I can not emphasize enough that retracting your front teeth to correct your bite would be a terrible mistake.  Visit several more orthodontists for opinions if you have not already and I think you will find similar opinions.