Sounds like you do the same type of riding you do. I call it hacking. I've used an English saddle for this type riding my whole life, so if you want an English saddle, it's definitely suitable for this type of riding. Most of the world hacks in English saddles.
I'm utterly clueless about Western bar sizes, but if your horse's back is considered wide, then you'll be needing a medium/wide, wide, or xtra-wide English tree. Keep in mind that all manufacturers have a different idea of what consitutes a medium, wide, etc. A Passier medium fits more like a Stubben M/W, etc.
Can you take a wither-tracing? Take it about 2" behind the last hair on the withers. This is about where the tree points will sit. Use a flexi-curve or coat-hanger. Take a look at the angle of your tracing where the tree-points will sit. If it's a little more than 90 degrees, it's M/W-ish. If it looks quite a bit wider, you're looking at wide or xtra wide.
Regarding the saddles you're looking at in that price range, a couple words of advice for avoiding a lemon:
If a saddle doesn't have a maker's mark or nameplate, it's usually a cheap Indian or Mexican saddle. If it also has thick, stiff leather, it almost certainly one of these saddles. Don't waste your money. They are generally poor quality, to the extent that they can hurt your horse and give you the wrong position, and are usually uncomfortable as well. Stick with saddles made in Australia, North America, and Europe. Some Argentinian ones are OK too.
The first saddle above is a Crump. The BT Crump co in the US (now out of business) imported some very nice saddles from England, Argentina, and (I think) Spain? The English ones were the Best, but all the Crumps are quite respectable. The girth may or may not fit, but it's nice that it includes leathers, irons, girth, and pad - that helps on the budget. I've never met an uncomfortable Crump.
The second saddle is a paragon saddle. It's a type of endurance saddle. Endurance saddles are great, and very suited to the riding you want to do. However, a good endurance saddle is quite expensive, unless you luck out. This one looks like the cheap kind, and since it has no maker's mark, I'm guessing it's Indian - stay clear.
Some good used brands to look for, which sometime come up in your price range, are: Crump, Crosby, Courbette, AG Felsbach, Sattlerei beim Kloster Schonthal, Wintec, Thorowgood, Bates, Passier, Stubben, HDR, Nice, Cortina, Rossi Y Caruso, anything English-made or German-made or Swiss-made, and more I can't think of right now.