I had a WISP unit upgraded for better reception and they used a Yagi
antenna, at least I guess it's a Yagi. Here's a photo.

http://www.netwifiworks.com/images/a.../Yagi/yagi.png

This doesn't seem to fit the mold in a couple of ways. The elements are
not spaced at all regularly. The spacing seems to vary around a
bit.

Yagi-Uda antennas can be designed with all sorts of variations
in element spacing. There are complex interactions between the
element locations and lengths, leading to numerous tradeoffs
between maximum forward gain, bandwidth, front/back ratio, and
cleanliness of pattern (i.e. size and direction of side-lobes).

But more importantly, I've read that the director elements are
*insulated* from the support beam while these are all welded.

It's possible to build a Yagi with the director, driven, and reflector
elements either insulated from the boom, or connected to it
electrically... and not all elements have to be of the same style.

In general, if you connect an element to the boom, you do it right at
the element's center (so that the ground connection is balanced).
Connecting the element to the boom has the effect of "fattening" the
element where it passes through the boom, and makes it look "longer"
electrically than it is physically... so, in order to keep its
resonant frequency unchanged, you must shorten it somewhat.

Welding the elements to the beam makes good sense for physical
longevity... there are no insulators to age and crack in the sun and
weather, and no possibility of intermittent current leaks or arcing
(which can cause noise or intermodulation problems in higher-power
use).

But more importantly, with the signal rising by 6 dB, the reported
background noise also rose 6 dB.

That could indicate a couple of things. It could mean that the
predominent noise sources affecting you, are in the same direction as
the WISP transmitter... and so they're being boosted by the same
amount as the desired signal.

It could also indicate that your old antenna or feed-line was
electrically "lossy", and that you were losing some signal (and
received noise) to resistive losses.