"every shipping rate within Canada will be going up significantly. "
NO NO NO NO
That is not the way HST works.
HST applies based on the type of service selected and the location of both sellers (in some cases) and buyers (in other cases)
Currently, if the seller lives in Ontario and ships a parcel to Nova Scotia, New Brunswick or Newfoundland and Labrador, Canada Post will charge:
5% GST on postage if the parcel is sent by regular parcel service or lettermail (based on the province of residence of the shipper)
or
13% HST if the parcel is sent by by XpressPost or Purolator (based on the province of residence of the recipient)
It makes no real difference to GST/HST registered sellers (most PowerSellers I suspect) as either amount is eligible for ITC.
The rules will not change on July 1st. Tax rates will change (from GST to HST) in
some instances if the seller or buyer is located in BC or ON.