Wolfram Language (Mathematica), 168 bytes
Min@(s=Select)[(f[f/@#~Partition~2,m=MixedRadix@{24,60}]-f[{v,f@p[[-2;;]]},m])&/@s[Permutations[p=#],24>(f=FromDigits)@#[[;;2]]>=(v=f@p[[;;2]])&&f@#[[-2;;]]<60&],#>0&]&
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