My answer is that if the law applies a no exceptions bans on vehicles entering a park and the ambulance driver eventually winds up in court over this then the judge would have no option but to find the driver guilty and apply the legislated penalty. Judges should not be able to unilaterally change a law.
The judge isn't changing a law. The judge that would convict under these circumstances is the one changing the law. A crime has not occurred here.
I will expand:
The whole point of language is to communicate; to reach a common understanding among the parties involved. Context is essential to any piece of writing, or for that matter all communication. A spoken word without context is just a sound. It only becomes something more when there is shared experience, tradition, assumption, whatever you want to call it that makes those sounds significant in a way both the speaker and listener understand. This can be on as basic of a level as "what language is being used" and then branches out to things like how a word is defined generally or within a subculture. Then there are issues of idiom, slang, and that language evolves. It gets extremely complicated. A sentence that seems simple to one person can mean something totally different to a different person because as a cultural matter they do not share the same understanding. Language is messy.
In this case the context is law, specifically criminal law. There are concepts that are implied within this context. In this situation the most relevant is the concept of necessity. The ambulance driver did not commit a crime because he had an obvious moral duty to drive into the park. It was a necessity to save a life. This concept is formulated a few different ways but this is the one where it's application is unambiguous regardless of how it is formulated. Within criminal law this and other concepts are baked into the common understanding of the words being used.
In this case within the Anglo/American legal tradition this goes beyond basic language concepts. Judge made a/k/a common law is a type of law and necessity is a pre-existing part of law and when a legislature passes a law it is understood to be within the existing legal framework. It is up to the legislature to say when they are changing the law or wanting a statute to be read in a way not consistent with existing law.
It is true that this statute says nothing about necessity. However that is only significant in that given the larger context it does not remove necessity from the existing law. One could read this statute and I guess take a narrow linguistic view applying only their understanding of context and assume that the legislative body intended to by silence exclude all existing common law doctrines from being used in the law's application, but that is the more tortured reading. You wouldn't be ignoring context. You would be substituting your own context.
Same in a more informal sense. We have a common understanding, or at least those of us with an iota of social intelligence have an understanding that a law meant to keep a people from driving through the park does not apply to emergency vehicles responding to an emergency. In the same way that if I tell the person driving a car to turn left I do not mean to immediately swerve left across traffic and hit a building. I mean the next intersection or other relevant pathway.
Without some context every word is a meaningless scribble. Textualism is a marketing word. What people who call themselves textualists are doing is selectively applying the contextual meaning they think applies and framing that as an absolute. It is a confidence game.
However, the police/prosecutors usually have some discretion about whether to charge someone or not and may decide not to charge the driver. There are probably hundreds or even thousands of outdated laws that are still on the books but are no longer prosecuted.
Long unenforced statutes are another thing that is handled within the context of law. That these statutes can no longer be enforced is the law in many jurisdictions. Civil law code jurisdictions (Louisiana for example) and some other jurisdictions (West Virginia for one) call it "desuetude." Some other jurisdictions formulate a due process construction. This isn't just a question of prosecutorial discretion.
In either case, pressure should be applied to the legislature to do their job properly and amend the law so that it deals with the question of when an emergency vehicle can enter the park.
The legislative body did do their job properly. The essence of the judiciary is to apply the general to the specific. While we do impose upon the legislature a duty to not be vague, that is a low bar and there is no expectation for them to address specific circumstances. The legislature is free to be as specific as they want,, but otherwise they leave the process of how to apply the law to the judiciary.
Even absent a clear idea of what the judicial branch will do the legislature is free to speak in general terms leaving the judiciary to fill in the blanks consistent with our understanding of justice. A judiciary that rejects this discretion in favor of a childlike hyperliteralism the unpleasant results of which are then blamed on the legislature is abandoning its duty.