MP4 karaoke "warbles" when tempo is increased

The program I use is Power Karaoke Pro. When I increase the tempo slightly, songs with a high bit rate (72kbps or above), it causes "warbling".
Will downloading and installing the Klite codec pack help? If so what settings would you recommend?

What you need is "pitch correction".

Media Player Classic (MPC-HC) from the codec pack has that functionality.

Options > Playback > Output > Audio renderer > select "Internal Audio Renderer"
Options > Playback > "speed step" controls the speed increase when clicking on the forward button in the player

And just how would I incorporate MPC-HC into Siglos Karaoke Professional Program?

MPC-HC does not integrate into other players. I am not familiar with the functionality of Siglos Karaoke.