##JavaScript (ES6), 118 bytes

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    ([a,...b])=>a+b.map(c=>'<><>'[k=(d=x-(x=p(c,36)))/13+2|0].repeat([d+26,-d,d,26-d][k])+'*',x=(p=parseInt)(a,36)).join``

###Test cases

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    let f =

    ([a,...b])=>a+b.map(c=>'<><>'[k=(d=x-(x=p(c,36)))/13+2|0].repeat([d+26,-d,d,26-d][k])+'*',x=(p=parseInt)(a,36)).join``

    console.log(f("abcdef"));
    console.log(f("zyaf"));
    console.log(f("zzzzzz"));
    console.log(f("z"));
    console.log(f("zm"));
    console.log(f("zl"));
    console.log(f("alphabet"));
    console.log(f("banana"));
    console.log(f("abcdefghijklmnopqrstuvwxyz"));
    console.log(f("abcdefz"));


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