Way to get Guitar chord text closer to the stave?

You can use any template you want, or no template, but I'm guessing you are creating what's normally called a lead sheet, so one of the two lead sheet templates would probably be a better choice overall. The plain lead sheet template creates extra-small music in the style of those fakebooks that cram as many tunes as possible per page. The jazz lead template creates extra-large music with oversized chord symbols in the style of most jazz fakebooks like the Real Book.

But regardless of which template you choose, or whether you create your score from scratch, the distance to the chord symbols is controlled by Style / Edit Text Style / Chordname, the vertical position parameter. You'll have to reload the score before the change will take effect for chords already entered.