This may not be the best solution but a possible alternative:
I have just recently started working on a problem with similar issues of
coordinate conversion and distortion, although the spatial nature of my
problem is somewhat different from yours. I am unbending a river so that
kriging is done in a domain that follows the course of the river instead
of going over land. I have converted the coordinates (which were already
in meters and on a small scale geographically) by applying a grid
generation scheme. (Gridgen is one software that can be used).
Grid generation is widely used in the field of flow simulation in channels
or around bodies where boundary conditions apply along irregular surfaces
(hydrodynamics, aeronautics etc).
The physical boundary is defined into four segments that correspond to the
four sides of a rectangle. An equal number of grid points are laid out
along each of the pairs of facing boundaries. Various algorithms (Laplace
transforms to linear interpolation, depending on the problem) calculate
grid lines between the extreme grid point pairs. The grid is generated in
the original coordinate system, so each sample has to be assigned to the
nearest grid point within limits of resolution and coordinate precision.
In flow field simulations, the differential equations and boundary
conditions are transformed based on the mathematical relationship between
the two coordinate systems. This is not necessary in this application, as
all grid points to be estimated are calculated before kriging.
Semivarogram calculation, modeling and kriging takes place in the
transformed space and the results need merely be mapped to the original
coordinate points corresponding to the initial grid generation output.
An excellent book on the theory is:
Numerical grid generation : foundations and applications
by Thompson, Joe F. (1985)
Published New York : North-Holland : Elsevier Science Pub. Co.
Gridgen is available from Pointwise for a free 90 day trial period:
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