For unarmoured single combat, what length of spear gives you an optimal balance between reach and maneuverability? Does it vary depending on stature or personal preference?

Between 6.5 and 8 ft...

8-9ft for most people, according to George Silver. He had a specific formula as well, based on reaching up to your limit and then adding the mount of space you'd want between your hands when wielding the spear/staff.

You want enough reach for a decisive advantage. More length beyond that will make your weapon less effective. But "enough reach for a decisive advantage" depends on what the other weapon is.

Against a not-too-long one or two handed sword (say, 34"/85cm or shorter blade), as short as 6'/180cm works (about 6' to 7' is ideal, IMO). But longer swords will make your reach advantage smallers. Short polearms will make your reach advantage disappear. The 8' to 9' prescription is a compromise against all sorts of weapons, including halberds.

Against another spear, you want a longer spear, but not too much longer. Perhaps 2' to 3' longer is best. So, 9' spear is better than 6' spear, and 12' spear is better than 9' spear. But 6' spear and 12' spear are about equally matched, and 6' spear is better against a not-long sword.

An 8' to 9' spear isn't unwieldy (or, at least, doesn't have to be - some examples might be), and won't be easy to grab if the spearman knows what he's doing. It isn't quite as fast as a 6' to 7' spear, so doesn't have quite as large an advantage against short weapons. But IMO it's still dominantly superior against short weapons.

Note that Silver considered his perfect length of 8-9ft superior to both shorter and longer weapons for unarmored single combat in the open. In fact he thought one person with a spear/staff of perfect length would have the advantage against two opponents armed with sword and dagger.

Antonio Manciolino apparently preferred longer staff weapons. He gave the lancia (12-14ft?) odds over the spiedo (roughly 8ft).

For a heavy-headed spear, it might be useful to shorten the weapon like that. 2' of extra spear behind you isn't a problem. But, in general, no need. The long spear is slower, but you get more reach, which gives you more time to move the weapon.

Using that formula, I came up with a 9 foot spear for me. I'll try to find a 9 foot shaft somewhere and see how it feels. I've never used a staff longer than 6 feet long before.

I tend to spread my hands out more instead of moving them up, if I want to trade reach for speed.

If I would hold a 6' spear with 2' between my hands, I can hold a 9' one with 4' between my hands. This gives me a *lot* more leverage to move the point with, making it harder to displace and easier to change through - and I still have a foot of extra reach.