Could an english saddle fitter do a good job on a stock horse and a western saddle?

If you were fitting yourself for a saddle, I'd stick with a stock seat specialist. But to fit the horse, if you can find a saddle fitter who is also a saddle maker, then the specialty shouldn't matter. Any saddle maker knows the basics of fitting gullet height and width, twist, pitch, and rocker in the tree that forms the skeleton of the saddle, and the rest is like the "flesh" that fills the saddle out over its skeleton. A saddle fitter who makes saddles should be able to evaluate the fit of any saddle. If none of the fitters in your area are also custom saddle makers, then I'd probably wait for one specializing in fitting stock saddles.

Here's a novel idea: Ask the fitter.

I would expect most English saddle fitters to have some idea about how to fit a Western saddle, but not all of them will be comfortable doing it.

So when you call to make an appointment, first ask if they can check the fit of a Western saddle. If they say no, thank them and call another. If they say yes, explain the issue, see if they'll come, and then make an appointment.

Only your saddle fitter knows if they're comfortable fitting a Western saddle. Ask them.

A saddle fitter will be able to fit a saddle, regardless of what type. They will still (or should) have a background in other types of saddles. They will be able to see where your saddle is creating pressure points or ill-fitting, they might not be able to re-flock or fix a different type saddle than their particular expertise, but you will know whether or not a saddle fits well.

Yep a inventory saddle could be an magnificent thank you to bypass, i became particularly youthful and my horse had a extensive bucking problem (and became over coming decrease back issues) and not in simple terms did my inventory saddle no longer harm his decrease back yet i became maintain as something and it became consistently a comfortable journey. It became in simple terms a cheapo one (like $3 hundred) yet it became in simple terms gently used so i could no longer inform you the way it would have worn over the years cos once I have been given the bucking taken care of I moved directly to a various saddle. i think of wintec makes inventory saddles (guy made) yet this is gonna value you till you will stumble on a 2nd hand one. additionally my bloke became no longer narrow in any respect (appy) so uncertain the type you will bypass with the greater healthful on your lady. sturdy success!

a saddle fitter should be able to fit any saddle to any horse

You're over-thinking it.

Either the saddle fits or it doesn't.