Could you please give me a product recommendation, as well as detailed instructions for cleaning and conditioning my Louis Vuitton Alma?

I have a four-year old Alma that I purchased pre-owned last month. When I purchased it, the handles were very shiny, with a medium brown patina. After taking the suggestions of others at The Purse Forum, I used alcohol-free baby wipes to clean the leather parts. When that didn't seem to clean well enough, I applied Apple Leather Care Conditioner to the handles with a Magic Eraser with light pressure. That didn't seem to do much, so I've been routinely cleaning the handles with baby wipes. Not only has that taken away the shine, but has left the handles dry with a chalk-like finish (the chalky appearance is mostly prevalent when I bend the under-side of the rolled handles). I've since applied a leather conditioner, as well as neats foot oil to try and restore the moisture and sheen - this not only didn't take away the dry appearance, but darkened the leather.

Is there anything I can do to clean the leather, and hopefully return that glossy shine/sheen? I thought the neats foot oil would help, but it has not. I also do not mind the patina, I am mainly concerned with cleaning and restoring a glossy finish. I've attached some pictures of how the leather looks now. I have also attached a picture of an area I didn't try to clean. (picture 5) This area has a nice glossy finish - this is what I would like all the leather areas to look like.


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(picture 5) This area has a nice glossy finish - this is what I would like all the leather areas to look like.
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