Dear Alastair:
An clarification of my analysis of your -1 to + 10 example:

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That is your model and it is one dimensional [call it x] that is it has one
venue.
Now add a dimension call it y that is infinite and perpendicular to your
example's x. This is an infinite number of venues. Add the y boundaries
at x = -1 and x = +10. Now randomly sample on this bounded xy plane. The
area of the plane below zero on the x dimension is the same as the area
above zero on the x dimension i.e. infinite = no bias as to sign mix of the
resulting random sample of reals on x.
{near the end of my post a further clarification}
What you seem to be saying re my approach using the above analysis of your
example is that either of the boundaries of the above plane in the y
dimension may meander between x = -1 and x = + 1. With this I agree.
Actually its essential. So what? The areas above and below the x = 0 line
are still equal i.e. infinite so a random sample in the xy plane over this
structure still produces no bias as to sign mix of the resulting random
sample of reals on x.
Hal