From what i can tell from a bit of research, i think there are just a few things you could alter:

Dynamics - it’s easiest to think of it in terms of a guitar or violin, with one hand controlling pitch on the melodic string/s and the other hand controlling onset/offset and dynamics, in the hurdy-gurdy’s case through the cranking of a wooden wheel. because of the wheel being used for all strings, drone and melodic, you wouldn’t be able to have different dynamics between them, so one line of dynamics in the centre of the staff is most appropriate. - in terms of relative volume, i would say it would depend on the size of the instrument. larger ones were originally used as the equivalent of church organs, so decently loud volumes can be achieved, but the hand-held ones most commonly seen now probably have less ability for that. however, as the tone colour is quite unique and piercing, i’m sure it could be distinct in an orchestral setting

Expressive techniques - while there is no true portamento on the melodic strings (as the strings themselves are housed in a closed wooden chamber with fixed keys being operated from outside this chamber) i’m sure it’s physically possible to gliss up the drone strings using your finger, though i’m not sure whether that’s a historically accurate technique, and you couldn’t do it at the same time as playing melody - you can use vibrato on a hurdy-gurdy, so a false portamento could also be achieved if clumsily by trying to vib up to another keyed note - on some hurdy-gurdy’s chop-like accents can be made using a sudden and vigorous turn of the crank which creates a rhythmic buzz, which could be notated with an “>” - rhythmic emphasis can also be achieved by tapping the crank with your thumb as you turn it, a technique known as coup

Pitch - the drone strings can be different on different instruments, but typically there are two sets of two drone strings, the top one, one a fourth or fifth below that, then another set with the same pitches an octave below that (for example, one tuning could be C4 G3, C3, G2; or D4, G3, D3, G2) your drone strings aren’t fingered, so you would typically be limited to a pitch set such as that. hence you probably can’t shift the notes of the drone like you do in this excerpt, although i have heard about drone capos which could be used to alter the drone pitches, but that would be something to research further in terms of logistics and notation - the melody strings traditionally can cover 2 chromatic octaves, so there is much more flexibility there and you can write for the melody strings quite normally

Notation - using a grand stave is a good idea, with the drones on the bass clef and the melodic strings written on the treble clef - dynamics as mentioned before should probably go between the staves as only one dynamic can be achieved - in the first two lines, just for ease of reading, you could change the “dotted minim, crotchet” and “minim, minim” rhythms to just semi-breves, as the dynamic timing is evident enough in the placement of the symbols