It is not a good idea to place the magnets too close together, but the spacing doesn't have to be particularly wide to avoid most of the leakage so in your case you will not see much increase in flux.

You do have more room for winding, but you are considerably increasing the length of the outer turns and this will offset some of your gain from room to use a larger section.

Reducing the air gap gives a higher flux density but reduces available winding area.
Small gaps have more dead space as we need mechanical clearance that we can't use.

Most of your benefit is based on the assumption that the wider magnet spacing will gain a lot of useful flux ( less leakage). with round magnets in particular the gain will be small and I tend to agree with Dan that it is better to loose a bit of flux and save on resistance. But You are right that to some extent you can trade the cost of magnets for the cost of copper.

We need another Jerry with enough patience to try the various combinations and really see what works best.  It is surprising how far you can change things with little effect on the results as long as you don't go silly.

The other temptation is to try and use the dead space in the centre of the coils. This requires overlapped coils and the advantage as seen at first is soon offset by increased lengths of turn and a painfully difficult winding process.

For example, the voltage on a turn of wire is proportional to the rate of change of magnetic flux encircled by that turn.  So, if we assume that the flux between the two opposing magnets is straight line, then two things become fixed ... first, the hole in the center of the coil should be no larger than the magnet, otherwise the encircled flux would become non-changing while the magnet moved within the "hole" and the voltage would try to drop.  Second, we'd want to space the magnets so that the "S" pole enters the edge of the coil just as the "N" pole begins to leave the center.  That would produce the maximium rate of change of flux for a given travel speed of the magnets.

Unfortunately all of this is complicated by the fact that the coil turns vary in diameter because they are wound flat and wide to reduce air gap.  So what you actually have is a bunch of turns (voltage sources) of different diameters hooked in series to make up the coil.  The outer turns are too large, ie do not meet the criteria of having a hole the size of the magnet.  The inner turns are too small, ie the "S" pole doesn't enter the turn until long after the "N" pole has exited.  The result is that the voltage never equals the theoretical and so we have to use "test coils" to verify what we're actually going to get.  The only way around this would be to use iron cores in the coils, so that you could assume that substantial flux changes occur only when the magnets pass over the cores, and this would then make all turns (inner and outer) have the same voltage peaking at the same time.

I expect that none of "our" (I'm being liberal here since I haven't built mine yet - my homebuilt uses a PM motor) alternators are likely to produce a true sinusoidal output, nor are they going to produce theoretical voltage, because the turns of a coil are not "in phase" with one another.

For example, I think a coil with a large center hole, coupled with wide magnet spacing, would produce high third-harmonic distortion.  While the magnet is moving across the hole, the encircled flux is not changing, therefore the voltage drops.  I could extend this argument to a large, wide coil with a small center hole because many of the individual turns still have large "center holes".  These turns contribute nothing to the coil's output while the magnet is merely moving within the center hole of that particular turn.