So if one sits down and determines the form of Maxwell's equations by careful measurement one might choose a complex anisotropic form for them? No thanks.

Of course. For all of physics, before SR as well as after, the physical content (IMO) of isotropy is:

1) assuming it leads to simpler expression of laws
2) any anisotropic formulation must be 'conspiratorial' in the sense that many different phenomena must be jointly anisotropic in a highly constrained way. This requirement for 'jointly constrained anisotropy', to me, is just disguised isotropy.

Only by virtue of peculiarities in the history of SR has the fact that you can't rule out conspiratorial anisotropy been prominent. Note, that many modern approaches to SR start by assuming isotropy, and homogeneity, and the POR, arriving at SR as one of only two possibilities, with no assumptions about light at all. With such an approach, the question of one way speed of light as distinct from two way, cannot even be asked.

IMO, physically significant anisotropy would be a universe where assuming isotropy forced complications, e.g. the need to add a special field that was wholly undetectable except for its hiding isotropy from being directly observed.

Yeah, I don't know. If a phenomena can't as a matter of principle be measured, I'm not willing to concede that it's part of physics. Suppose I have two beam splitters separated by a distance L. They are angled so that when a short light pulse entering from the left a fraction of the pulse is directed to a sensor a distance 1000L from the pair along a line perpendicular to the line between the two splitters. When a pulse enters from the left the sensor will detect two pulses L/c+ apart in time. The splitters are then angled so a pulse entering from the right will yield two pulses L/c- apart in time. Why isn't this a one way measurement?

Well, playing devil's advocate for conspiratorial anisotropy, that one is easy. The two almost perpendicular paths are ... almost perpendicular. Deviation about 1 part in a thousand. Then, the small difference in light speed along the so called perpendicular legs, accumulated over a very long path length, compensates for the difference in light speed each way between the beam splitters, such that the signal reception difference and the receiver is the same as under the assumption of isotropy.

No they don't, for the fast direction, they increase the signal delay, for the slow direction they decrease it, such that the observed deltas match. Perhaps 'whatever' means you worked this out.

Yes and no. If I assume a physically reasonable anisotropy of the form ##c(\hat{n}) = c_o + \alpha \hat{n}\cdot \hat{v}## for propagation along ##\hat{n}## and where ##\hat{v}## is some fixed direction in space, then all I need do is place the sensor's 1000L in the plane ##\hat{v}\cdot\hat{n}=0## and the beam splitters along ##\hat{v}##. In this case the errors cancel as I claim because both long arms are retarded or advanced by the same amount and the anisotropy on the short leg is maximum. So this form of anisotropy is detectable. I assume the anisotropy in this discussion isn't physically reasonable .

Oh well. This isn't my night.

I would still need to accept terms in Maxwell's equations that are unneeded. Ain't going to happen.

I disagree. For light traveling in the fast direction, the signal from the first beam splitter arrives a little early compared to average c, while signal from the second beam splitter arrives a little late. The result is to augment the detection interval compared to the implicit reduced travel time between the splitters. For light in the slow direction, the signal from the first splitter hit arrives late, while from the second arrives early, which reduces the detection interval compared to the implicit augmented travel time.

For the record I concur. As it's been pointed out several times this "phenomena" is merely a coordinated change and therefore moot. An anisotropy in light speed would do violence to Maxwell's equations. However, any self respecting experimentalist (played by myself) would never discover this in the underlying physics because we deal with observables which this is not.

The way out of this dilemma is simply to recognize that the one way speed of light and the synchronization are two parts of the same convention. It makes no physical difference what convention you pick, so pick an easy (isotropic) convention. Since it is merely convention you are automatically justified in doing so, and you recognize that people who want to make extra work for themselves are also entitled to pick a silly convention.

Hm, is it really pure convention? I doubt it. Using SR as a spacetime model, which includes the assumption of isotropy and homogeneity of space for any inertial observer, of course implies the consistency of the standard Einstein-synchronization convention, but as soon as you take gravitation, and thus GR effects into account, you'll find deviations (like the gravitational deflection of light running close to the sun, as was one of the classical confirmations of GR, making Einstein the first superstar of science when this effect has been observed by the Eddington collaboration in 1919). So the deviation of spacetime from homogeneity (due to the presence of a "heavy body" like the sun) is objectively observable and cannot be cured by pure conventions. Of course you can, according to the (weak) equivalence principle, always find a locally inertial (and thus isotropic and homogeneous) frame of reference but, at presence of non-negligible gravity, never a global one!

But, I didn't understand, why I should do that. Of course, you can in principle choose any kinds of coordinates, but how does it help to understand the determination of the speed of light a la Roemer?

It shows that using a model in which light speed is anisotropic, that the Roemer measurement would measure the two way light speed. That is, it would not exclude the ability to consider light speed highly anisotropic.

I'm glad we're getting back to the original question. One of the messages that the OP didn't have time to read points out that if you want to know two things - the one-way speed of light and the synchronization convention - you need to measure two things. Since there's only one measurement, I can pick a synchronization convention and get any one-way speed I like.