Brian: I play square neck dobro and have two instruments, a Wechter-Scheerhorn and a custom dreadnought size. Both are 25" scale. The scale length affects the string tension at pitch, so the 25" scale instruments have a lower string tension compared to a standard 25.4" scale for acoustic guitar. Your Gold Tone is a 25" scale.
The standard dobro tuning is GBDGBD, with the D of the first string one step below the high E on regular guitar tuning. leading to lower tension just due to pitch. (other tunings are fun also - I use a D tuning for some tunes DADF#AD and it's a blast for the keys of D and E). The thinner the strings, the lower the tension but also a thinner, "plinkier" tone with less energy to drive the cone for tone and volume. The lower tension using very light string gages at the dobro tuning does not support the bar as well, which could also lead to intonation challenges.
Standard dobro string sets use a 0.016" high D string. I use a "Scheerhorn" set with a 0.017" D and 0.019" B. The slightly heavier set does have somewhat higher tension, but the trade-off is a cleaner tone with stronger fundamental. (It is also harder to do behind-the-bar string bends ala Jerry Douglas).
My square neck strings are about 7/16" above the fretboard at the nut. Both of my instruments are "fretless" with maple inlay for fret position. You will need about this much clearance above your fretted board to allow for a dobro capo (I recommend the Scheerhorn style capo). It is common to capo at the 2nd fret to play in the key of A for bluegrass and fiddle tunes.
All of the above is more than you asked for

In the end, do you trust the strength of the neck joint on your Gold Tone? Hopefully your existing nut can be removed intact, and then you can install a new taller nut with no radius and with the string slots appropriate for some heavier strings. Just to clarify, raising the nut height does not affect the string tension since the string length and pitch are fixed, it probably just affects the force pulling on the neck joint. As Peter stated, you aren't really worried about the truss rod and action above the frets. (Nut extenders can mess up the intonation by moving the nut position towards the first fret. It's possible to compensate with bar position but it makes it trickier to stay in tune).
You will need new saddles with no radius also (I'm assuming your Gold Tone has split saddles with a gap for the cone tension screw). The typical 12" or 14" fretboard radius for a standard guitar is just about impossible to play in tune with a bar across the strings in dobro style.
Have fun experimenting! Fortunately, nut and saddle changes are easily reversed should you decide to switch back to standard guitar configuration.
All my babbling on above didn't address your string gage questions, but hope it helps you with some dobro information!