There is a maxim of geopoesy: who makes the world makes the rules.
In a secondary world, a world of your own devising, an invented language would not need to "enforce" subjective idealism at all. Only one thing is required, and that is to "set the dial" of your subcreation to subjective idealism.
In that world, only the mind and mental constructs have true existence. The language a mind devises for itself to communicate (within itself) and assuming the mind that exists is a human mind, will arise to describe its experience.
I think your semantic primes would probably be sufficient to describe both the realia of the mind-being's existence: the 1s pronoun, the concrete verbs such as "think", "know" and "believe", the qualia of phantasms created within the mind. Because sunsets and wine do not exist.
If the world you subcreate is, in actuality, a typological copy of the primary world, where things outside the mind have actual existence, then you run into the exact same issues I dealt with when your question was about the primary world itself.
Such a language, I hold, would not be able to "enforce" subjective idealism in any meaningful way. It would not be able to overcome the steak and eggs problem.
Original response to unedited query (regarding subjective idealism within the primary world) retained for historical purposes:
Subjective idealism is the monistic metaphysical doctrine that only minds and mental contents exist. It entails and is generally identified or associated with immaterialism, the doctrine that material things do not exist. Subjective idealism rejects dualism, neutral monism, and materialism.
How could my to be constructed language be restricted to such view of reality?
A very interesting thought experiment! But I believe is simply not practicable.
I don't think a language of any kind will be able to enforce that kind of (quite silly) perspective of reality.
In order to pull it off, I think you would have to first, absolutely and positively convince yourself that Berkeley was a) on to something and b) that a) is The Something.
Now, reason and common sense inform us that things do actually exist. Things outside the mind, things outside of mental construct. I can sit my weary bones down on a chair and be thankful that chairs exist. They're not mental constructs. They're articles of furniture made of wood and designed and built to be sat in. That's reason and common sense refuting Berkeley.
Now, I had a look at Mr Berkeley's picture in that article. He looks pretty well fed to me. Not emaciated, not dehydrated. I'll just bet he enjoyed a good steak and eggs for breakfast!
A true subjective idealist would also have to be a practical breatharian, because food does not exist. It's an insubstantial construct of the mind.
For your language to really function, you too would have to become a breatharian. You know: immerse yourself in the culture! Let us know how far you get in the practical application of this kind of philosophical language!
Specific to your last point re objects: I think, since objects do not exist and are therefore irrelevant to the thought and being of the mind, you could probably get away with a language where all substantives (apart from the 1s) are reduced to a single pronominal stem.
Trees don't exist, so you wouldn't really need a word for "tree". I don't exist, so you don't need a word for "elemtilas". This post doesn't exist, so you don't need words for "stack exchange" or "invented language" or "post" or "forum".