Both the Audio Research LS2B and BAT VK-3i are excellent choices, especially if you're seeking warmth and musicality. The BAT VK-3i is known for its rich, tube-driven warmth and spacious soundstage, while the LS2B offers a more neutral, detailed presentation but still retains some tube warmth. Since you're looking for balanced connections with your ML 27.5, the VK-3i might be a better fit as it’s fully balanced, whereas the LS2B is hybrid balanced.
Using unbalanced-to-balanced cables is fine, but you may not fully benefit from the balanced design. Given your preference for warmth and jazz listening, the BAT VK-3i would likely deliver a more engaging, non-clinical sound.
By the way, I have a BAT VK-3i for sale in excellent condition. If you’re interested, feel free to reach out for more details or to discuss it further.
Good luck!