Hi and welcome to the community. I know much about GERD, and I don't think it can cause slurred speech but I'm not a doctor or speech pathologist. GERD can do alot of muscular things to the esohagus but in all the years dealing with it with 2 of my 4 children having it serverely and also being on the GERD community, I haven't heard of slurred speech. I'd ask your doc for certain though and post on the adult GERD community here.
C~
The twitching sounds like some other neurological issue, definitely NOT GERD. The twitching could be caused by Benign Cramp Fascilation Syndrome, however BCFS (to my knowledge...) doesn't have slurred speech as a symptom. Look at other neurological diseases for starters, such as MS or ALS. I am not a doctor, this is only my own personal opinion. Let us know if you find out any further findings, I'm interested in your results.
Mark