The problem with your board is that L has to work the second shift on two consecutive days, but in your hypothetical case, L is working the first shift on Monday and Tuesday. Thus, it won't work.
If G and J are on the same day, the two possibilities we have are
HKGHG LLJJK (On Thursday, H and J can switch with each other)
and
GKHHG JLLJK (on Thursday, H and J can switch with each other)
Does this make sense? Let us know if you have any questions!
