Electronic – If you have two identical but oppositely wound inductors does the inductance effectively cancel

Your assumption that the core flux cancels out to zero is not valid because you don't have perfect coupling between L1 and L2. If you had, then the inductance for the series-additive connected inductor should measure 120 (not 90) uH, because inductance is proportional to the square of the number of turns, and you're essentially doubling the number of turns. Likewise, you would measure no inductance for the series-opposing connection. Note that even if there was no coupling you would still measure 60 uH for the series-additive pair, so it seems there is a fair amount of leakage flux.

In the opposing flux configuration, the effect on the circuit is similar to replacing the coupled inductor with two separate inductors having much lower inductance values. As a result, the current ripple is higher, and the associated core losses are higher.

The Japanese (back when 50/60Hz mains transformers were still viable) would often use a lighter gauge of wire for the 'upper' half of the 230V (or whatever) winding. North American makers, in my experience, not so much.

I don't think bifilar winding would be good because of insulation considerations when they are in series. It's fine when they're in parallel (and sometimes used because of skin effect or just to get a heavier gauge), but I think bad practice to depend on the wire insulation for much breakdown voltage. If you break the input to the transformer with a switch, a lot of voltage will appear across the primary winding, and half of that would be wire-to-wire with a bifilar winding.

You can't connect them in parallel because of the CT, but it wouldn't be a very good idea anyhow- the different number of turns means the transformer would quickly overheat.