Hi, firstly, don't mean to sound picky but it is hard reading a big block of text like that. Breaking up your paragraphs & using more punctuation is helpful
Short answer is a definite no. You don't ever ride a horse that is hurting, or you suspect is hurting, *unless* under vet's(or body expert's) advice. As we can't possibly know the facts remotely as well as anyone seeing the horse, let alone an educated & experienced bodyworker, can't really say much more than that.
But a few things came to mind...
What is a 'natural equine physical therapist'? I've never heard of the lable & TBH I'm a bit skeptical of people/products with the term 'natural' in them, because it's a bit like 'lite'... a too often effectively meaningless marketing term. Unfortunately, equine bodyworkers are completely unregulated, like farriery, so there's no guarantee of a basis of knowledge or skill level. So they may well be fantastic & very knowledgeable, or got their 'license' off the proverbial cereal box. Not that I reckon people that haven't done extensive formal training & certification are necessarily 'bad' at all, but if you have no way of judging either, I'd be inclined to look for a registered chiropractic *vet*. If they're registered as such, they must either be a vet or human chiro first, before doing an extensive course to specialise in equine chiro treatment. therefore, you're guaranteed of an extensive & specialised education before they touch your horse.
If it were just because he'd been put in a hill paddock, he must have been VERY unfit before - was he stabled full time or such, for the guy to think that? Chance of slipping over while playing is a LOT more likely, as is being saddle sore from you putting it on him wrongly, or otherwise badly fitting, so especially in the face of those things, the first suggestion is kind of not worth even mentioning.
If it is tight muscles, then it's possible it's nutritional - for eg. lack of magnesium/too high calcium will cause that.
If you got his saddle 'refitted', possibly that was the problem, that it still doesn't fit well(unfortunately 'saddle fitters' are like farriers - just because they do it for a job doesn't mean they're necessarily good at it), especially if you were fitting it wrongly & they didn't even ensure you knew where to place it on him. I hope it was all well explained by the bodyworker, but if it slips out of place so readily, either it still doesn't fit very well, or your horse has one of those bodyshapes that requires a breastplate &/or crupper/breeching to keep it in place.
In addition, if the saddle needs more padding, why is that? Is it Western or English style? Are the panels too hard, the saddle too big, too little of a channel...? And while I believe sheepskin is a great 'medium' between horse & saddle, it doesn't provide a lot more padding, and a 'half pad' in the way they're frequently made, with a doubled section of sheepskin at the front & back, if these parts are under the saddle(rather than sticking out, fore & aft), can cause a saddle to 'bridge', the extra thickness creating ridges.
And re what 'exercises' can you do(when you have the go-ahead to ride) because it's getting boring... go for a trail ride. Include obstacles to go round, through, under, over. Practice riding without reins(don't just go 'cold turkey' tho!).