Adding many sounds to a video file at specific frames
Alright, more googling found that ffmpeg is definitely the solution to my issue!

ffmpeg -i inputvideo.mp4 -i inputsound.wav -filter_complex "[1:0]adelay=leftchanneldelay|rightchanneldelay[delayed];[0:1][delayed]amix[mixout]" -map 0:v -map [mixout] -c:v copy -c:a aac outputvideo.mp4


This line allows me to easily determine where in the video (down to the millisecond, which is more than precise enough with each frame equaling 20 milliseconds) I wish to place the sound; wrap it in a loop inside a batch file (or whichever method you prefer) and off you go!

Edit: A more fully-featured solution written in Java, which only creates the audio file (to allow you to add it manually):

package javaapplication4;

import java.io.IOException;

public class JavaApplication4 {
static String delay;

public static void main(String[] args) throws IOException, InterruptedException {
    String a = "0";
    String c = "1";
    String temp = "";
    String basePath = "C:\\Users\\Desktop\\Stuff\\FFMpeg\\";
    String fileIn = "blockbreak";
    int[] delays = {2740,5760,51381,61040,84520,109600,113660,156640,311260,312820,314100,443800,735120,740540};
    Runtime.getRuntime().exec(basePath + "ffmpeg.exe -y -i " + basePath + fileIn +".flac -filter_complex \"[0:0]adelay=" + delays[0] + "[mixout]\" -map [mixout] -c:a flac " + basePath + "output0.flac").waitFor();
    for (int i = 1; i &lt;= delays.length - 1; i++) {
        delay = "" + delays[i];
        System.out.println("" + (i) + "/" + (delays.length - 1));
        Runtime.getRuntime().exec(basePath + "ffmpeg.exe -y -i " + basePath + "output" + a + ".flac -i " + basePath + fileIn +".flac -filter_complex \"[1:0]adelay=" + delay + "[delayed];[delayed][0:0]amix=inputs=2:duration=longest[mixin];[mixin]volume=6.0201dB[mixout]\" -map [mixout] -c:a flac " + basePath + "output" + c + ".flac").waitFor();
        temp = a;
        a = c;
        c = temp;
    }

}

}


I increase the volume of the sound by 6.021db each time as ffmpeg seems to lower the volume when encoding; this isn't a perfect number, but it's close enough that the difference in volume between the first and last sounds in a file that's a few thousand sounds long ends up being around 1 db.