I have to say that Effex is the answer as well----the conditioner, not the cleaner. Sadly, it contains whale oil. I found this out after I had purchased a bottle, so I used up the bottle and then switched to olive oil as needed.
Oh, and my saddle wasn't new when I got it, but it had been sitting around for years (I think) and I got it from a pawn shop. It's a Hennig, so the leather is doubled and wears like iron. It's noticeably softened up with time
I bought a new English made dressage saddle with an XW tree last summer, so I feel your pain. I also use the Effax in the brown container. Brought it home, sat with it in front of the tv and applied, rolled, waited til it dried, and repeated.
As for the stirrup bars, I'd be careful with that. If they are that tight, they may need to be pulled out by a fitter.
I was sent a new saddle on trial and had a horrible time getting stirrups on. In three days my horse had a super sore spot on his back where the stirrup bars had been digging into his back from being too tight. I was told "it happens," they pulled them out, and it was sent back to me. It was then very easy to get the leathers on and my horse was fine in it.
My saddle was made by a different company, but if it's as common as I was told it was, I'd keep an eye on that. Check underneath and see if you can easily feel the bars through the panels.
Every other new saddle I tried was not difficult to get the leathers on and I use Prestige's nylon lined, calfskin covered webber-type without the buckle. They are thick, but I don't notice them under my leg like I do with a pair that has a buckle.
When I got a new Albion, I used the Albion cleaner and balsam on it per the saddle fitters advice. She also told me to never oil it, just use the conditioner. The saddle is super- duper sot and supple now. I conditioned it daily for a few days before I even rode in it and it broke in- no time at all. Have Fun!
This is exactly what I did with my new Albion, I conditioned it all over for a few days before I rode in it and then made sure to condition it after each ride so buttery soft and comfy right away. Plus I love the smell of their swiss formula congrats on the new saddle!!!