Kirkburton registers go back to 1541.You can download vol 1 of Frances Collins's transcripts from www.archive.org (search in the search box in the top left, not in the http://http:// search box).This is a PDF which has been OCRed so you can search the contents.Vol 2 is on Google books but isn't OCRed so you just have to work through the index.
Almondbury registers don't go back quite that far but they do extend well into the C16th.The early volumes are available only in hard copy from the Yorkshire Archaeological Society.Later volumes are available on CD-rom from the Huddersfield Family History Society http://www.hdfhs.org.ukhttp://www.hdfhs.org.uk
Emley parish registers only go back to 1600.
My family history back to 1600 seems to be concentrated in K'burton & A'mbry.Both have missing periods, particularly in the C17th.However it's quite clear that there is also under-recording, at least in Almondbury.In part this may be due to the fact that the parish is a large one and there were a number of chapels of ease, one of which Slaithwaite was shared with Huddersfield to which it belonged and Holmfirth ditto with Kirkburton.It's possible that stuff went missing by not being copied from the chapel registers which don't necessarily survive that early.However there are also missing marriages which should have taken place in the parish church itself.
There were a great many Kaye families in the area at all levels of society.The Kayes of Woodsome, however were important and although I haven't had occasion to look at them in detail (my Kayes were much more humble) I know they're amongst the best documented families of the area.You will find them in the Almondbury PRs but 1544 is just a little too early.