Add ruling authority to the Netherlands East Indies?

I'm adding notes to the Netherlands East Indies and see P1 to 9 and 39 to 44 are missing. For these notes we miss a few ruling authorities:

For these from 1815. Example: http://www.banknote.ws/COLLECTION/countries/ASI/NIN/NIN0001.htm

I'll suggest either “British Interregnum (1811-1816)”

or 

William I (1815-1840).

I'm leaning mostly towards William I, since his monogram appears on the notes.

For these from 1846. Example:

http://www.banknote.ws/COLLECTION/countries/ASI/NIN/NIN0039.htm

I'll suggest William II (1840-1849)

Edit:

I think William I need to be added regardsless, since we also miss a ruling authority for P17 to 24. Example:

http://www.banknote.ws/COLLECTION/countries/ASI/NIN/NIN0017.htm

Tagging referee, in case they have something to add: @Linketake42 

Thanks :D

Sources:

https://en.wikipedia.org/wiki/French_and_British_interregnum_in_the_Dutch_East_Indies

https://en.wikipedia.org/wiki/List_of_monarchs_of_the_Netherlands

I'm more partial to the British Interregnum suggestion myself. 

So maybe all three? British Interregnum, William I and William II? 

Forgive me, I'm apparently blind.

William I and II are added. But we still need some for the 1815 notes.