I have no idea which saddles have removable blocks other than synthetic and I never use them but would probably recommend you look at the Ideal Jessica as a relatively flat simple dressage saddle which are often advertised second hand if you are planning on buying without a saddler involved, if using a saddler get them to bring a selection so you can get a feel for what suits you as well as the horse.
I don't like knee blocks either, they really interrupt my aids.
K&M are good saddles and have nice wide gullets for all horses, not just wide cobs. I have used LM Saddles for about 10 years or so now and I do really like the saddles. I would look for a nice broad wide gullet with plenty of panel to distribute your weight without restricting the shoulder..... easier said than done.
Thats why I suggested the Jessica as it has very little in the way of blocks, one of my clients had a serious hip problem and it was the only saddle that she tried that she could ride in, we had one made with a narrow twist to make it even more comfy.
Hidalgo. The system is extremely flexible. It is not treeless (as many people believe) and has exchangeable panels to fit them to the length of the horse while the seat size can be fitted to you. The knee blocks have velcro an can be taken off. The saddles are very comfy and available in lots of different styles.
My daughter has a Hidalgo Venice dressage saddle and I have an Iberian model for hacking - so comfy and safe.
I've got a GFS Monarch, real leather and their "more reasonable price range". The knee blocks are on velcro so you can move them to suit and the gullet is adjustable. Mine is in an xw at the moment but I believe they go as high as xxxw though I think you need to buy the wider saddle in the first instance. Leather is nice and is kept really well and is very comfortable, I've been using it for a few years and have the same in the GP.