While my disability was based on both psychological and physical conditions, my Long Term Disability Insurance company refuses to even consider the physical aspects and I have no clout with them. They cut off my benefits after the "usual" 24 months.
Has anyone else any experience with this?

Lots of good folks are messed with everyday like this by their LTD insurer. You gotta fight 'em.

Many disability policies have a two year cap on mental health disabilities. Courts have ruled these terms as ambigious. They do not apply if the mental condition is organic. You need to talk to a lawyer asap.

And most lawyers you go to will want substantial money up front. Don't pay it. Get someone to take it on contigency. I have a claim in federal court. It's been there 5 years!