I might consider using ffmpeg to increase the volume, and then burn the output to CD. Do note that ffmpeg is a command-line program, so that might make it a little harder to use. You can do this using something like:
ffmpeg -i input.mp3 -map 0:a -vn -af acompressor=threshold=0.022:attack=20:release=500:ratio=3.25:link=maximum:makeup=9 out.flac
The above example assumes your mp3 is called “input.mp3”, and will produce a dynamic-range-compressed file called “output.flac”, which you can burn (dynamic range compression is similar to normalization, and should give you the result you’re looking for, without clipping). If your burning program doesn’t support the flac format, you can use wav. (I don’t recommend using a lossy format like mp3 as your output, since doing so will result in reduced quality. You should use something lossless like flac, wav, alac, etc.) You’ll have to do this with each mp3 you plan on burning, though.