Hello Alpine! I'm sorry it took me this long to find your need for support! I too was in your shoes just a few short weeks ago.
I am now just over 10 days post-op from LIS and Anoplasty surgery. I had the EXACT same problems as you are experiencing - one or two large fissures with skin tags and internal papillae, several smaller ones wreaking havoc in other areas, and my sphincter was experiencing extreme stenosis (too tight).
My CRS suggested the Anoplasty along with the LIS to help mostly with the stenosis (it adds a little extra skin) in addition to helping by replacing the chronically bad tissue with good. I will say, that with all the frustrating stuff that has accompanied my recovery, my sphincter is sooooooo much less tight. I don't have leakage anymore, I have complete control, and BMs are a breeze to get out. Before, as soon as a BM would start my body would go into shock and my sphincter would just shut down and close up tighter than a bank vault on a national holiday. It would pinch off whatever was coming out and I'd have to just wait until I calmed down to try again. Now, when I feel the urge to go, I just go. It's like years ago before my fissure. Quite lovely really (Thanks for inadvertently reminding me of one of the positives of my surgery, btw...).
If your surgeon suggest LIS with Anoplasty, feel free to read my experience in the general forum (I can link it later when I'm not on my phone). I have also kept a blog of my experience at an external site if you click the 'www' button under my user name.
I really hope you are able to find comfort that you are among wonderful people here. They are all so helpful, and as a newbie myself, I will do all I can to help too. Best of luck to you for your upcoming appointment. If you have any questions, please don't hesitate to ask.