Peaceable Projects Inc. is a U.S.-based non-profit group that brings the vast resources of the wide world together with the ongoing needs of the people who live, work, and travel on the Camino de Santiago pilgrim trail network in Spain.
The Camino Frances (and other routes) are becoming increasingly busy each year and April/May is when numbers start to build up. Also next year is a Holy Year (when the feast of the St James, 25th July, falls on a Sunday) and there isn't another one until 2021 so there will be lots more pilgrims than usual walking.
Obviously the business of a Holy Year has its own excitement particularly for Spanish pilgrims and the local authorities along the way are putting arrangements in place (school and church halls etc) to accommodate increased numbers. I suspect next year it will be very much a case of going with the flow and sleeping where you can or walking on to the next albergue.
If this isn't your thing you could think of another route or another year.
The Camino will be busy next year indeed, though April may be slightly less crowded than the summer months. If you could push back earlier to March that might help. Otherwise, a possible mitigation would be to arrive as early as possible to the refugio in which you want to stay each night...the later in the day you arrive, the less chance for a bed. Buen Camino!!