When I transitioned from english to western way back when, I ordered a trail saddle with no horn because I wanted a simpler look. They sent me the wrong saddle (essentially the same thing, but WITH a horn), but said I could ride that one until the new one showed up. They both fit so well I negotiated to keep them both, so was in the unique situation of having both options.
In the end, I preferred the horned saddle, since it made it really easy to have horn saddle bags. I grew to like the look too…when in western saddle, make it look the part.
Since western saddles are all I ride now, I quite like having a horn whether roping or not. When practicing your centered riding, having the ability to lightly touch the front of the horn to center your seat is really valuable. While possible to do in an english saddle too, it’s not quite the same feel IMHO.
BTW, FQH bars etc is completely meaningless in the grand scheme. It’s no different than trying to expect one dressage or jumping saddle “medium” to be the same between mfgrs. The sooner you forget you even heard the terms, the better.
Last, $300 isn’t even much of a budget used, so please be very careful shopping. Find someone local who you can use, or you’re going to end up with a hollow fibreglass tree from India and a good hospital bill when the saddle fails.
On the bright side, your horse is really nice, and should be an easy fit. She’s not nearly as downhill as would make much difference to fit. I can’t help in saying WHAT would fit, but around here a trip to a used saddlery place would likely end up with a bunch of options (though not many at the price point you mentioned).