In advanced English syntax and stylistic sentence improvement, the revision of faulty coordination, misplaced modifiers, dangling participles, and ambiguous pronoun reference requires rigorous morphosyntactic restructuring. Consider the following four advanced propositions regarding sentence improvement and reordering: I. When an introductory participial phrase or gerundial adjunct begins a complex sentence (e.g., 'Walking through the botanical gardens, a rare orchid was spotted by the researcher'), it must structurally and logically share the exact semantic subject with the matrix clause; otherwise, it constitutes a classic dangling modifier requiring complete subject reorganization (e.g., 'While walking through the botanical gardens, the researcher spotted a rare orchid'). II. In sentences featuring correlative conjunctions (such as 'not only... but also', 'either... or', and 'neither... nor'), strict grammatical parallelism must be enforced by ensuring that the syntactic categories following each correlative element are completely heterogeneous and asymmetrical (e.g., pairing a finite verb phrase with a nominal gerund clause). III. When reordering jumbled sentences within a coherent academic paragraph, initial sentences typically introduce broad thematic or theoretical frameworks, whereas subsequent sentences deploy cohesive ties, anaphoric pronouns, and transitional adverbial connectors (e.g., 'consequently', 'furthermore', 'conversely') to ensure logical progression and rhetorical unity. IV. In sentences containing restrictive versus non-restrictive relative clauses, non-restrictive clauses must be enclosed entirely within commas and introduced by the relative pronoun 'that' rather than 'which' or 'who' to indicate supplementary non-essential information. Identify the option that correctly evaluates the grammatical, syntactic, and semantic validity of propositions I, II, III, and IV according to standard English grammar and Sentence clause structure principles.