くらいには is na-adjective くらい（だ） + particle は.
As na-adjectives exploit nominal particles as their "conjugations", here the くらいに form is treated as its adverbial form (連用形). Also note that くらい itself has both facets as a noun and an adjective. The noun form くらい has adverbial usage, too. However, bare adverbial くらい and くらいに have some difference in usage.
苗が一週間で10cmくらい成長した。 the sapling grew (approx.) 10cm in a week.
苗が一週間で10cmくらいに成長した。 the sapling grew to (approx.) 10cm in a week.
But in all other times when the distinction of the "final level" and the "changed amount" is vague, the difference wouldn't be critical:
もう歩けるくらい回復した。 ≒ もう歩けるくらいに回復した。
Now the second problem is は. It's the well-known topic particle, and particularly in this context, it adds to a nuance of "at minimum". But what might be more important here is that は clearly divides くらい and くらいに into noun and adjective/adverbial usages.
?? もう歩けるくらいは回復した。 (loses the adverbial reading)
So, this ～くらいには can be translated as "at minimum to the level/degree —", or in more natural way, "(easily) enough to —". You can never reword it using くらいは.
In philosophical parlance, it should be translated as "subject". The translation "subjectivity" only works in the following definition.
Some information, idea, situation, or physical thing considered true only from the perspective of a subject or subjects. (Wikipedia)
All other meanings of subjectivity (see the link) should correspond to 主観性.
But in daily language, it's used to roughly denote "one's own (personal) feelings/stance/understanding" without much lofty connotation. In this specific case, it indicates the idea that he thinks "僕は今、その次元を超えた邂逅を果たしていた" (in the top of this paragraph).
By the way, the meaning of 支配 is a little hard to grasp. I guess it's intended to be "overwhelm" or "engulf" here. Your "compel" is a good choice too, but in that case "compelled to (have the idea)" is felt more suitable than "compelled by".
This sentence is hard to understand correctly. The structure is doubly ambiguous on where the clause ～くらいには should settle on.
- ～くらいには……理解していた (I was aware ... enough to —)
- ～くらいには……～ようなものだ + ない (it is not [something like ... enough to —])
- ～くらいには……～ようなものではない (it is something [not like ...] enough to —)
Though the option 2-1 is less likely from the context, the sentence is still roundabout and ambiguous.