For what it's worth I walked the Frances, Muxia, Finisterre routes last year starting from StJPDP late May. I used a silk bag liner and don't recall being cold on any night.
There were blankets available in every municipal Albergue and I stayed in.
The coldest I ever felt when walking was on a few early mornings at altitude.
I too am walking the Primitivo around the same time as you. Based on my experience last year I will use the silk liner again, with the thought in mind that if I need to I'll sleep with some clothes on or use a blanket if available.
Good thing is, it's a Camino, so, I won't know if I will need to until it happens, if it does
.
Like someone on here once said regarding the weather (Falcon I think), "the weather will be the same as last year but on different days"
Maybe go with the 'lightest' sense of adventure on this one Cheryl?
Buen Camino