Third & final opinion. Lower bleph with or without fat transfer? (Photo)

I do cosmetic eyelid surgery, fillers, and I fix other surgeon's work.  You will not benefit from lower eyelid surgery with or without fat grafting.  You do have an under eye circle and an early midcheek groove.  This is, by far, best handled with artfully performed hyaluronic acid fillers.  To be honest, getting this right is fussy and a total art form.  Very few injectors can perform the service you need and are knowledgable about what is needed for maintaining the service.  Done correctly, you will be able to avoid surgical procedures for the lower eye area for another decade or more.  More importantly, as unsatisfactory as your under eye circle may be, you have many lower eyelid elements that are youthful and wonderful.  These will be utterly wiped out and destroyed with lower eyelid surgery with or without fat grafting.  You will regret this choice and almost immediately you will look older from this intervention.  You don't need and won't benefit from a lower blepharoplasty and/or fat grafting. I am strongly advising you not to do this to yourself. 

You are right to be concerned as this is a delicate  area.  More photo views would be helpful.  You do not appear to require  skin removal, so any surgical procedures would be best performed from inside the eyelid to remove of reposition fat  but avoid a scar. Fat transposition seems  like a good option but the possibility of insufficient fat, and maintaining proper placement during  healing can affect the final outcome. You could still need touch up fillers. The more conservative option would be sequential fat transfer with PRP in small amounts or fillers which at least can be dissolved.  Remember,  aging is ongoing and will require periodic touch ups and maintenance.   Other factors that contribute to transient eyelid swelling (like allergies etc. ) should be considered.    

Thanks for the excellent question and posting a photo! 
You bring up a "hot topic" within plastic surgery regarding lower blepharoplasty technique. Depending on which surgeon you ask, you'll likely get a variety of answers. Though it seems more papers are coming out these days describing techniques of lower blepharoplasty utilizing fat transfer, there still seems to be no consensus. 
Based on your picture, there are tear trough deformities on each side which can be corrected by either technique. Some surgeons will transpose/reposition the fat from inside the eye onto the cheek after doing the surgical dissection- this can help blend the eyelid-cheek junction into a smooth, softer look. Others- during a formal blepharoplasty- would inject fat around the bone just underneath the eye to help eliminate the sharp transition at the tear trough, or if you have a flatter appearing cheek (can't tell from the picture) then adding fat to this area can improve aesthetics. Another purported benefit of fat is that it may help improve the dark pigmentation of the tear troughs- though I'm not sure if there's definitive data on this. And finally, other surgeons would recommend against surgery altogether for isolated tear troughs and offer fillers only instead. 
I'm not sure there is a right answer- excellent results have been reported with both standard lower blepharoplasty as well as fat transfer, in addition to filler alone. You may opt to pick the surgeon whom you are most comfortable with and whose results you most admire. Each technique will likely deliver good results if performed by a qualified, safe surgeon! 

I prefer lower blepharoplasty with fat grafting when you have prominent fat pads and under-eye hollows (often with cheek deflation at the same time).  This doesn't mean its the only approach.  Fillers will also fill in the hollows but then you're committing to yearly injections to maintain the results. Ultimately, you should find the surgeon you trust and have a good rapport with and arrive at a plan together.  It can be hard to find a surgeon that is sufficiently experienced with under-eye fat grafting.

Based upon the photographs you submitted and without a formal examination, I would recommend a transconjunctival lower blepharoplasty (surgery done without a visible scar behind the eyelid) with a fat transfer of the excess lower lid fat into the areas between the eye and the nose noted as the tear trough. That would avoid future hollowness and correct the puffiness as well. The problem with fillers is that it is temporary and will make the whole underneath eye area look puffy. Good luck in your area.

The beauty of this forum is that you will get different answers from acknowledged experts in the field.  The problem with this forum is that you will get different answers from acknowledged experts in the field and that you will not get the tie breaker opinion you are seeking.  Personally, I think you would have an outstanding result with lower blephs with Fat Transfer.  To make your decision even more difficult, I am not a fan of under eye fillers and I am not a fan of fat repositioning and I have done all of these techniques many, many times.  Good luck!