StreamVoice has recently pushed the boundaries of zero-shot voice conversion (VC) in the streaming domain. It uses a streamable language model (LM) with a context-aware approach to convert semantic features from automatic speech recognition (ASR) into acoustic features with the desired speaker timbre. Despite its innovations, StreamVoice faces challenges due to its dependency on a streaming ASR within a cascaded framework, which complicates system deployment and optimization, affects VC system's design and performance based on the choice of ASR, and struggles with conversion stability when faced with low-quality semantic inputs. To overcome these limitations, we introduce StreamVoice+, an enhanced LM-based end-to-end streaming framework that operates independently of streaming ASR. StreamVoice+ integrates a semantic encoder and a connector with the original StreamVoice framework, now trained using a non-streaming ASR. This model undergoes a two-stage training process: initially, the StreamVoice backbone is pre-trained for voice conversion and the semantic encoder for robust semantic extraction. Subsequently, the system is fine-tuned end-to-end, incorporating a LoRA matrix to activate comprehensive streaming functionality. Furthermore, StreamVoice+ mainly introduces two strategic enhancements to boost conversion quality: a residual compensation mechanism in the connector to ensure effective semantic transmission and a self-refinement strategy that leverages pseudo-parallel speech pairs generated by the conversion backbone to improve speech decoupling. Experiments demonstrate that StreamVoice+ not only achieves higher naturalness and speaker similarity in voice conversion than its predecessor but also provides versatile support for both streaming and non-streaming conversion scenarios.