Is it possible to get a half-feral cat spayed?

Since there is nothing to do where I live atm (I'm working on moving away!) I decided a few months ago to try taming a few of the feral cats that wander my complex. I currently have two kittens and an older male that I assume is their father coming to me when I call them for food (meat too old or fatty for me to eat personally). The older feral cat is still rather cautious with me, but since the two kittens have known me for nearly all of their young lives they have grown very trusting of me; in fact I literally have them eating out of my hands. They also allow me to pet them, know their names, and even have learned the importance of taking turns and sharing. I think I did pretty well considering I was rarely go out to see (when I have food to get rid of or am really bored) and have only been half-heartedly trying to earn their trust.

However, I did the math today and realized that it's been 3-4 months since I first started my attempts at domesticating them. At the time they were with their mother, but were old enough to be coming out and exploring on their own; which I believe means they should be getting close to sexual maturity. This doesn't bode well for the female kitten since the only unaltered toms with the immediate vicinity of her 'home' are her brother and her father. The complex I live in already has far too many stray and feral cats, so it would be best for everyone if she was spayed before she went into heat.

Is there a good way to arrange this? She trusts me enough that I could probably pick her up and throw her in a cage to drag her to the vet before she had time to realize she should be upset, but I really don't want to ruin all the trust I've built up with my half-hearted attempts at taming her by doing that. I'm also not inclined to go through the pain and hassle (and expense!) of doing it. Is there another way to arrange to get her spayed..preferable one that is convenient for someone who really isn't certain he care enough to bother ;P