[Tagging] How to tag access restriction on interstate highway crossovers?

[Xavier]

By "interstate highway crossovers" I mean small bits of road that 
connect the two carriage ways of a US interstate highway and are signed 
as "Authorized Vehicles Only" (at least in Virginia they are signed 
this way).

An example is here:

http://openstreetcam.org/details/1253343/475/track-info

If you look at the left edge of the photo, you will see part of the 
pavement of the small way that connects to the other traffic lane of 
the highway.  Zooming in on the sign visible just behind the curved 
guardrail at the far end of the crossover in the photo will show the 
"Authorized Vehicles Only" restriction language.  Clicking on the "edit 
in Id|JOSM" links will open the location so you can see the aerial 
images of the "crossover".

The "Authorized Vehicles Only" sign really translates to: access 
allowed for police, fire, and rescue vehicles.

A way mapping this feature would obviously be highway=service.

And an initial access=no tag to prevent routers from deciding to try to 
use it for U-turns.

But looking at the wiki values for the access= key there are two 
'close' values for "access allowed for police, fire, and rescue":

1) private
2) designated

However the description of designated indicates that it is a different 
meaning than what is meant here.  That leaves private, but somehow 
'private' seems not really a good fit at the same time.  It is not 
really 'private' as in privately owned, it is public, but restricted.

So is access=private correct, or is there a better tag that I've not 
located yet?