Today breeding Gouldians is quite easy as the birds are now totally domesticated.
I presume you have a true pairs and they are at least relatively young.( I am not trying to be smart asking the above)
I normally put my boxes into the aviaries in December. This is when my birds are in breeding condition and will produce chicks.
This year I put them in last weekend(good rainfall) because the hens are in condition and on checking Tuesday there were 8 pairs building and possibly eggs now.
I do not even attempt to put boxes in unless the hens beaks have change to grey/black.
If the hens nest and lay while their beaks are normal colour the infertility is huge if not 100%.
Very few birds would even think about breeding if they a stuck away in dark conditions, infact even low to the ground is far from ideal.
While the Princess are unlikely to hurt them the simple fact is they are far too large for the Gouldians. I really think common sense should prevail.
I do not think it is your birds that are the problem but the conditions they are being held in are not really ideal for breeding.