I just run the two r's together and have no problem. To me, the lack of agreement between subject and verb is far more jarring than the flow of saying "there's" verus "there're."

I quite agree, nikeblack -"therur" rolls off the tongue perfectly as well as "there's."

As to finding Gareth difficult - that's probably because it is a Celtic name introduced into a largely Saxon environment, and the two never did mix all that well, in any situation. Try saying "Gareth Thistlethwaite" - without pausing for a drink in the middle!
Do any Welsh words that start with a "th" sound? If not (as I believe) then that sort of problem wouldn't occur.