I recently picked up a copy of Lorraine Lee Hammond's Barley Break: An Elizabethan Songbook with Arrangements for Appalachian Dulcimer.

In this book (and The Magic Dulcimer) she uses four different tunings. I will list them in order from bass to treble using the scientific notation (as in D4 A3 d3):

Tuning I

G3

D4

d4

Tuning II

G3

D4

c4

Tuning III

A3

D4

c5

Tuning IIII

A3

D4

c4

The question: In order to not repeat the first mistake I made, tuning up from D3A3d4 to  D3A3a4 (instead of tuning correctly to D3A3a3) and breaking the thinnest string, what would be the best way to actually tune these? It doesn't have to be in a specific key- they would be tuned to each other. 

The bass strings in all tunings go down, so not an issue.

The middle strings all go up from A3 to D4, which is only 3 notes.

The treble strings stay the same or go down except for Tuning III, where it goes up to C5, which is a 6-note increase.

Can the middle strings handles going up 3 notes?

Tuning III scares me...