The steam idea is the way to go.
For measuring the border, take 3 measurements across the quilt. & top to bottom.
Ex.
Across measures 36,,, 35-1/2, & 36-1/4. Add these = 107.75 ÷ 3= 3
5.92.
Round that # off to 35.875", cut the top & bottom that length.
Repeat this for the length.
I usually put the top & bottom borders llast, but in this situation the quilt needs too be supported on the sides, so I would add the sides last.
When steaming the quilt, bring the fabric to that measurement, pin securely to the border when you stay stitch.
Be sure to cut the borders on straight of grain, to support the edges, or you will end up with a wavy quilt.