I am of the opinion that one should use leather-specific/dedicated leather cleaning and conditioning products on such interior material.
Since you are inclined to use something readily available and over-the-counter leather-care products, I would highly suggest going to AutoZone or O`Reilly Auto and getting some of the Griot`s Garage leather care products, like their 3-in-1 Leather Care. If they have the Odor Neutralizing Leather Cleaner in stock, buy and use that first before the Leather Conditioner.
I would NOT suggest buying or using Lexol Leather Cleaner and separate Conditioner "twins", even though the cleaner has the glycerin for cleaning you mentioned. Yes, I admit having used Lexol twins in the past on some nicer leather, but I have been "schooled and educated" from others in this forum about not using Lexol, hence my suggestion for using Griot`s Garage Leather Care products.
The Medallion Premium Leather Care product you mentioned is, I assume, a Meguiar`s Mirror Glaze "premium" product. I used that as well, but that was even before the Lexol twins. It was OK in its day, but I have moved on to Griot`s Garage leather care products. I also assume the word "discovered" means you`ve seen it somewhere in an automotive store, but did not purchased it yet.
One other suggestion for an readily available, over-the-counter (OTC) leather product is Chemical Guy`s leather care available at Walmart. I know some in this forum are NOT keen about using Chemical Guy`s products, especially since it comes from a big-box store like Walmart. I have no experience with it, so for me to say it it "better" than using Lexol is unfounded and has no merit. Your buying and using it means you would be "the guinea pig" as to how well it works. It`s just a suggestion and option of an OTC product.
One caviat to watch out for is using a strong ammonia-based cleaner or a degreaser soap or Goo-Gone on coated leather or using Mr. Clean Scrubbing Pads to remove/abrade embedded dirt or blue-jean color transfer or ink pen marks. DON`T do it. You can (and will) permanently discolor or scuff mark your leather. And yes, specialty leather cleaning products for such stains are available via internet resellers and not generally OTC (local leather upholstery shop(s) being the exception).
As far as a readily available, over-the-counter soap for cleaning, on coated leather some have used Woolite Cold Water Soap (Yes, the laundry soap for fine,delicate fabric and clothes). I have done that as well, using a 1:7 diluted ratio (1-part soap: 7-parts water) but that was also a long time ago. This suggestion came from long-ago Autopian contributor Scottwax who stated that back in the 60`s Cadillac actually suggested using Woolite for cleaning their leather in their cars, according to the owners manual.
Again, I think there are "better" leather-specific cleaning products available today. Not sure I am telling the truth? Key in "Woolite" is the Search box yourself and look at ALL the thread topics from the early days (2002-2007) of this forum on using this product on leather.
As far as using 303 protectant on coated leather? DON`T. It might say it can be, but I would not. It`s really is designed and formulated for vinyl and plastic, NOT coated leather.
Still unsure??? One other suggestion is to go to an automotive upholstery shop in your area and ask them what they suggest. They deal with leather all the time and they may have a product line that they use for sale to their customers and general public.
OR a nearby Harley-Davidson dealership and see what they suggest for a leather cleaner and conditioner, albeit for black leather seats.
You question about cleaning and conditioning coated leather is a common newbe topic. You are not the first and you wouldn`t be the last.
There is also the school of thought that coated leathers should NOT be conditioned, only cleaned, as the conditioner attracts dirt and dirt is THE killer of wearing out and discoloring leather, especially in the seams and stitching of the leather seat. You can "research" that topic yourself. Cleaning the seams and stitching with a soft tooth brush (yes, there are specialized brushes for this purpose) goes without saying, and is probably THE most over-looked part of thoroughly cleaning leather seats and upholstery. One tip before you start cleaning leather is to vacuum it by phyisically pulling the seams apart with your finger and brushing them and then vacuuming them,again spreading/pulling the seams apart with your fingers on one hand and vacuuming with the other. A lot of work? Yes, but it is easier to vacuum and remove"dry dirt" first to than soak-up or wipe up "wet dirt" later when shampooing/cleaning.