I've been wading through translations of the relevant legislation and there are a few vectors that I am still exploring. There is an allowance for modified vehicles that might be applicable, but I need local guidance from an expert so I'm hoping the local classic car club can help (they have been enthusiastic from an initial contact).
The class seems primarily targeted at things like cab and frame trucks that a power or telephone company may put a custom box setup on, but I don't see anything that excludes the concept of a custom vehicle.
I do know from a site that lists cars for rent for model shoots and films that there are some other 356 replicas registered in Portugal but it is unclear if those are beetle titles or something else. They could also be grand fathered.
While the typical route is full EU licensing, there is an allowance for national only licensing which may allow some leeway as well. There is also a classic car classification but that does not seem viable. Not only do you need approval from FIVA I think it is called, and a log book, but the vehicle must be over 30 years old and only travel 500 kms or less a year. So basically parade use. Not what I need.
So with the right finesse perhaps a national only title under the modified vehicle category could be possible.
I was pleasantly surprised to discover my IM has a catalytic converter which I didn't realize. That definitely helps as they license and tax (initially and annually) based on engine displacement and emissions. 2.5L is considered a large engine there as well.
Overall, despite the enthusiasm for cars there at the citizen level, the regulations around cars are some of the stricter ones I've seen, combined with heavy taxation for new and imported used vehicles. All part of the hero's journey.