You need to use map scale rather than map width and so some calculations, e.g.
gmt begin arctic_map png
W1=$(gmt mapproject -R0/360/65/90 -Js0/90/72/1:25000000 -Ww)
H1=$(gmt mapproject -R0/360/65/90 -Js0/90/72/1:25000000 -Wh)
W2=$(gmt mapproject -R0/360/55/90 -Js0/90/72/1:25000000 -Ww)
H2=$(gmt mapproject -R0/360/55/90 -Js0/90/72/1:25000000 -Wh)
dx=$(gmt math -Q $W1 $W2 SUB 2 DIV =)
dy=$(gmt math -Q $H1 $H2 SUB 2 DIV =)
gmt coast -R0/360/65/90 -Js0/90/72/1:25000000 -Dh -Wthinnest,black -Ir/faint,lightblue -B0
gmt coast -EGL,IS+c -R0/360/55/90 -X${dx} -Y${dy}
gmt coast -Dh -Wthinnest,red -Ir/faint,lightblue
gmt coast -Q
gmt end show