As I read it, ASVE's will have to re-register as a "Custom Vehicle." 
"The license plates must include the word or words   "Classic," "Custom Vehicle," or "Street Rod," or a similar   designation, as appropriate."
In order to get the plate, you gotta get inspected one more time:
"On initial registration of a 
custom vehicle or street rod, the owner must provide proof, acceptable to the department, that the custom vehicle or street rod passed a safety inspection that has been approved by the department."
THEN you no longer need to get inspected:
"Sec. 548.052.  VEHICLES NOT SUBJECT TO INSPECTION. This   chapter does not apply to: …
(2)  a vehicle moving under or bearing a paper dealer in-transit tag, machinery license, disaster license, parade license, prorate tab, one-trip permit, antique license, 
custom vehicle license, street rod license, temporary 24-hour permit, or permit license;"
Good news, I guess .. but like everything in this hobby .. some assembly required 
And ... if all this is a pain, you can stay an ASVE and get annual inspections. BTW, I'd check with my insurance agent and see if it matters which way you go ...
Sam