I agree that 新字体 is preferable to 简体字 for exactly the etymological reason you cite, the thing with 言 only being simplified when it is a radical in 簡體字 really irritates me (especially since it is not a difficult or slow radical to write anyhow), and there are more examples than just that. For me I practice with 正體字 most often despite being more familiar with Japanese; so my preference goes 新字體 > 正體字 > 簡體字.

P.S. adding lang attributes on those spans where you compare versions of the characters would be nice, though I get that you have to choose just one of several, when a character is nearly identical in two or more countries. In my browser it also fixes an issue where despite serif being in your CSS font stack, it will select a sans-serif/gothic font by default if no lang attribute is set.