What large "package" is carried by this large spider underneath itself?
It's a Huntsman spider. The genus is  Heteropoda but not sure of the species (pingtungensis?) Yes, it is an egg case she is carrying.
Ask a local if it is the white barred spider, LaYa 喇犽, Mandarin is 白額高腳蛛. If so then it may be veratorias as in below article.
Wikipedia article on one species at
https://en.wikipedia.org/wiki/Heteropoda_venatoria
If you get more good photos, put them on wikipedia or somewhere. Until then, here's Heteropoda venatoria (Fam. Sparassidae) from here:
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