This comes from the headmaster's message on the school website:
"If this ethos appeals to you and your son, then the RGS would be the right place. I look forward to meeting you."
I suggest you take him at his word - how about a good old-fashioned letter by snail mail, addressed to the headmaster? It'll only take a day longer, won't get "lost" and you should at least get a response. Perhaps you'll be treated more favourably if you ask to be shown around after the main exam season is over - come to think of it, that might explain why nobody is willing to entertain your request at the moment!
I would find it hard to believe that any school that values its reputation would not be willing to show prospective parents and students around during a normal school day - perhaps you just got through to the wrong person who was having a bad day?
Sorry I can't offer any advice or opinions on the schools themselves.