Following up on this topic as I just had a conversation with my paper rep...
I was ordering a pallet of Finch copy paper, and he said they won't have it in stock until May 14 - almost 2 weeks out, and most of what they ordered from the mill is already sold. He mentioned at one point a few months ago, there was no 80lb gloss text available in the US (from the mills), no distributor could get their hands on it from any manufacturer, so they had no way to restock their warehouses for a time.
Aside from mills converting their machines to make other products, the lumber industry is also affecting paper production. Some mills own their own forests, but those that don't are having to deal with increased profitability from lumber. More trees are being converted to lumber instead of pulp, so raw material for any paper is in shorter supply. And because some mills are converting to other products, people are turning to other brands to fill the void. This places more demand on those mills, who are having a difficult time keeping up with the drastically increased demand.