I use a Victorinox (Forschner) Fibrox Cimiter for trimming hard fat too. I've tried everything up to and including uber
sujis to trim packers, and didn't think they did a better job than the Forschner; or an Old Hickory either for that matter. Another nice thing about a Forschner is that if your knife gets "borrowed" at a comp, it's no great tragedy. It does nearly all coarse meat work as well as anything else, and is damn near impossible to hurt. There are good reasons why Victorinox Fibrox are the gold standard for professional butchers, going beyond the handle.
If you feel thinning is necessary, and don't mind bench stones, you can thin your old blade very effectively on a cheap, (Norton) Coarse India, then either get a very serviceable finish on a Fine India, or go back to your EP. The best profile is 15* flat on both sides, and plan on heap much plenty steeling during use.
If you don't feel comfortable about leaving the EP in favor of bench stones, get an EP 120 (very fast and coarse) or a (fast enough) 220. It's ridiculous to throw away a perfectly serviceable knife because it's dull, and just as ridiculous not use your EP because you're concerned about the price of expendables.
My experience is that tough soft Euro alloys sharpen better on oil stones anyway (but not with oil!); and prefer an Arkansas finish to anything else for both edge quality and durability. I don't think Mark carries Arks cut for the EP, but you can get a Surgical Black Ark (ideal for your purposes) cut for the EP from Best Sharpening Stones
The two negative comments I will make about your Cimeter are that (a) 12" is an awkward length for trimming without taking a lot of meat away accidentally; and (b) Chef's Choice sharpeners are fine, but it's not quite accurate to call what they do thinning
. A trizor
edge may be many things, but none of them are thin. Fine for your purpose, but let's not kid ourselves.
If you want an expensive suji you should have one; but it won't cut the fat (h/t Ron Popeil), better than your Forschner.