You need to look at this in very simple terms.
You and your brother did something quite complex ( which I don't think you truly understand) and now its a question of moving on. To all intents and purposes your brother owns nothing. He is not on the deeds. You are the only one on the deeds. You own the property. BUT if you want to cut him out, he has some comeback because he has a Deed of Trust. Mind you, a Court ( if it ever came to it) may very well say that that was a stamp duty evasion trick and refuse to deal with it.
So why don' t you just sell half of what is yours on the face of it to your girlfriend and gift what is paid to your brother?
Example. Property worth 400K. Mortgage is 350K. Equity is 50K. Half is 25K. You sell half share 25K to g/f for 25K, she takes responsibility for half the mortgage, you give 25K to brother, brother tears up Deed of Trust........etc.,etc
mf