That is very small text to work with. I could not match your font so there are differences.
I went straight to Text-to-Path then turned the text layer off. Selections came from Path-to-selection
The first layer is the only 'funny' one. I filled the selection with the gradient then to remove the odd stray anti-aliased pixel, inverted the selection and cut.
The outline layer 2 is a straight stroke selection line size 1 with anti-aliasing off under layer 1
The background, layer 3, selection, grow selection 4 pix fill with gradient.
To hide the odd anti-aliased pixel, the outline goes over that (layer 4) again stroke selection, anti-aliasing off, line size 1 pix.
edit: just seen the odd pixel that will need a bit of hand editing
I went straight to Text-to-Path then turned the text layer off. Selections came from Path-to-selection
The first layer is the only 'funny' one. I filled the selection with the gradient then to remove the odd stray anti-aliased pixel, inverted the selection and cut.
The outline layer 2 is a straight stroke selection line size 1 with anti-aliasing off under layer 1
The background, layer 3, selection, grow selection 4 pix fill with gradient.
To hide the odd anti-aliased pixel, the outline goes over that (layer 4) again stroke selection, anti-aliasing off, line size 1 pix.
edit: just seen the odd pixel that will need a bit of hand editing