Here's something that has bugged me for a while. I know how to seed the random function via the current time:
The problem that I have with this is that the randomness changes only once per second with this method, which is not truly random. Is there another method that changes the seed value more often per second, or is there not a standard function that does this?

you could use the clock() function, which outputs the number of clock ticks since process start. The (slight) problem is that this can be the same on two different instances of the process (unlikely). To remedy that, you could combine time(NULL) and clock(), by addition or multiplication or something.

Sorry for my ignorance, but when you say "the number of clock ticks", is the clock ticking faster than once per second? If not, the question remains.

short answer: yes.

medium-length answer: yes, 1000 times per second in fact.

long answer: allow me to cite a few pertinent quotes