I started on March 31st from Sevilla last year and think anytime from mid-March to end of April is a good time to go. I did find the weather quite chilly at times, mainly from wind chill, particularly north of Salamanca. If I was doing it again I'd leave mid April. That said, it was a cold spring last year!
I was in Salamanca for Easter Sunday and had no problem finding a bed having which I booked only a couple days before. I didn't notice any influx of pilgrims during holy week - maybe this is more of an issue on the last 100km to Santiago sections e.g. Sarria, Tui etc.
There was a really nice number of pilgrims. Never too many to make impersonal like the Frances, but never too lonely either except from Granja to Astorga. Most people don't go this way anyway.
Hope you enjoy it. I am also going to be on the VDLP again when I arrive in Merida from Almeria via the Mozarabe. I am then walking up to the Sanabres. I won't be leaving Almeria until end of March so you'll be well ahead of me!