Thank you, everyone, for your replies. We will probably end up adopting another cat when we move into a bigger place, but we are also still considering breeding our cat on top of that. So no, we will not be neutering him any time soon. We've had him for over a year without any behavioral problems up until now, except for this howling over the stray cat. We don't feel right neuetered our cat as he has no physical interaction with female cats whatsoever, so we don't have to worry about kittens at this time. So unless he develops a medical condition that neutering would correct, he's staying intact. At least for the immediate future.
I think my best bet is to contact an animal shelter here to pick up this stray, as the past few days she's been spending 100% of her time on my balcony (except when she goes down to the courtyard to potty). She is Very pregnant and I suspect she'll give birth within the next week at most. Unfortunately there is only one local no-kill shelter in my city and they are overcrowded and undstaffed, but I don't see what other choice I have.