I was going to ask a few of the same questions. Are you sure temp and humidity is wrecking your paper, or does the basement darkroom have a light leak. Or maybe safelights. Or, are your factory sealed papers ancient to begin with?
Yes, I routinely break up boxes of paper and re-wrap in sheets of 25 or 50, in extra black envelopes lying about. Sealed with duct tape, spare cardboard envelope, then two trash bags withas much air sucked out as possible, then taped as well.
Do not open a frozen package of paper until it is thawed and up to room temp, for obvious reasons.
I do not refreeze thawed packages, partly out of fear of condensation again, and partly out of superstition.