I'm with Glory, use white vinegar and let it soak in the machine for about an hour. Then wash and do that several times (like 3-4). I had a vintage 1940's leather jacket I did that with that had a musty smell nothing would solve (including professional leather cleaning and deodorizing). Then I put it in the dryer on low heat for about 2 hours and then left it outside to air dry for about 2 weeks.
Yeah, a lot of work. But it worked. Soaking and washing with vinegar like 4-5 times and almost a month's worth of air drying --but sooooooo, worth it. This was a really rare brand and model of vintage moto leather jacket.
Also, leather specialists vary greatly in their abilities to clean leather effectively. I've got one here in L.A that when I've sent newly acquired vintage musty leather jackets to and specified clean AND deodorize --the funkiest smelling vintage leather acquisitions have come back completely odor free. So don't give up hope.
You may be right in assuming it's the leather itself. It may also be the tannery leather smell you're experiencing. A lot of leather jackets from Morocco, India and Pakistan have a VERY distinct odor to them from their tanning and dying process that my sensitive nose finds offensive. (When I was in Morocco at the tannery they actually give you mint to hold up to your nose to counteract the awful smell while you're there visiting --and you can smell the tannery section from blocks away).
Usually a combo of speciality cleaning and deoderizing along with leaving them to air out eventually causes the tanning process smell to disappear.