<p>As a family of tweakable block ciphers, HALFLOOP is standardized in the interoperability and performance standards for medium and high-frequency radio systems published by the United States Department of Defense. Although HALFLOOP-24 has been destroyed in real-world practical attacks, seeking stronger attacks from the structure of ciphers against two larger variants of HALFLOOP is to be further explored. Since HALFLOOP has a property of smaller internal states compared to master keys, it leads to a low diffusion in the key schedule. Considering that related-key boomerang attacks have a significant effect on such ciphers and can even achieve full-round attacks, we evaluate the resistance of two larger variants of HALFLOOP against related-key boomerang attacks in the paper. First, we propose a more efficient model to search for sandwich distinguishers of ciphers with non-linear key schedules. Specifically, we derive more constraints rather than simple relationships in the internal linear layer to further restrict the appropriate distinguishers into a smaller space. In addition, we utilize the ladder switch effect in the related-key model to guarantee the differential transition with probability one among the master key quartet, thereby avoiding possible weak-key attacks or invalid trails. Second, applying the model to HALFLOOP, we propose a full-round related-key boomerang attack on HALFLOOP-48 and nearly full-round related-key attacks on HALFLOOP-96. The relevant results demonstrate that the security of two larger variants of HALFLOOP is weak in related-key scenario. Therefore, in addition to the serious flaw brought by the tweak, the low diffusion in the key schedule algorithm is also worthy of attention.</p>