no need to re-bias anything. I'm not sure you will get much more headroom but it will be good to see how you get on. I have used 5751's to reduce the gain in a pre-amp and make it more flexible but I didn't get more cleans at higher volumes.
The dials on the amp may go higher before it distorts but the volume that the distortion starts to appear will probably be about the same. Experiment and see how it goes, it may be just enough to satisfy your needs.
Changing the speaker to a more efficient one can help also. If you have the matching Vox V110NT cab then I would consider changing it, it really isn't very good, the 1x12 TV cab is way better.
You just can't get a lot of clean headroom with a very low powered amp.
Nice avatar... I can see why an AC30 wouldn't be suitable in your household at present ;-)