I've got a 4ohm amp and 8 ohm speakers, but the setup doesn't go as loud as i would like. The 8 ohm speakers are sensitive to 87dB and are rated at 100 watts, I'm thinking of getting 6ohm ones at 88dB and 70watts. Would there be a significant increase in output if I make this change?

No. I would upgrade your amp, not your speakers if you want more volume. Unfortunately, if you want the music to be twice as loud, you need to supply 4 times the power.

The key question is how many watts can your amplifier put out at 8 ohms?

Hmm, the amp was pretty expensive as it was, don't fancy paying for a more expensive one. It's 75w at 4ohms, so 37.5 watts at 8ohms.
It could go louder, but I was advised not to turn the amp up past half way as it would damage the speakers through distortion.

I wouldn't hesitate to try turning it up more. Just listen very carefully for distortion. If that still doesn't produce the volume that you are looking for, think about looking into a pair of 4 ohm speakers.