Cross-chain technology facilitates the interoperability among isolated blockchains, where users can transfer and exchange coins. While the heterogeneity between Turing-complete (TC) blockchains like Ethereum and non-Turing-complete (NTC) blockchains like Bitcoin presents a significant challenge for cross-chain transactions. Payment Channel Hubs (PCHs) offer a promising solution for enabling TC-NTC cross-chain payments with high throughput and low confirmation delays. However, existing schemes still face two key challenges: (i) significant computation and communication overhead for variable-amount payment, and (ii) limited unlinkability, i.e., vulnerable to the abort attack. This paper proposes EC2P, the first TC-NTC cross-chain PCH that achieves variable-amount payment unlinkability while resisting the abort attack and minimizing reliance on non-interactive zero-knowledge (NIZK) proofs. EC2P introduces two protocols: the NTC-to-TC and TC-to-NTC payment protocols. The NTC-to-TC payment protocol replaces the traditional puzzle-promise and puzzle-solve paradigm with a semi-blind approach, where only one side is blinded and the blinded side’s interactions are eliminated. This achieves unlinkability and resists the abort attack without NIZK. The TC-to-NTC payment protocol enhances the paradigm by utilizing Turing-complete functionality to constrain the inability to carry out an abort attack. Through rigorous security analysis, we show that EC2P is secure and variable-amount payment unlinkable while resisting the abort attack. We implement EC2P on Ethereum and Bitcoin test networks. Our evaluation demonstrates that EC2P outperforms both in terms of communication and computation overhead and reduces communication costs by 3 orders of magnitude compared to existing variable-amount methods.