For reference:
SAAMI .308 Winchester
GO: 1.630 in.
NO-GO: 1.634 in.
FIELD: 1.638 in.
FN FAL
GO: 1.6325 in. (FN & Brit/commonwealth. Canadian is 1.6315 in.)
NO-GO: 1.638 in.
FIELD: 1.640 in.
7.62 NATO (M14 US MILSPEC)
GO: 1.6355 in.
NO-GO: 1.638 in.
FIELD: 1.6445 in.
Note that .308 Field = 7.62 No-Go, with 7.62 Field being 0.002 - 0.0065 greater. While your rifle is "technically" still safe by 7.62 specs, tightening it up is definitely a good idea.
You're going to need to remove your existing locking shoulder anyway, so press it out with the same cheap (but perfectly serviceable) Harbor Freight 2-ton arbor press that you're going to need to press in the new locking shoulder.
That locking shoulder allows your bolt to close on a 1.638 inch gauge. Measure it, and you'll have a good idea of what size locking shoulder you're going to need to bring your headspace down to 1.63xx (whatever you decide to set it at).
You could just order up the appropriate sized LS and skip the pin gauge(s), since you have HS gauges and can actually confirm proper headspace. However, I'd spend the $75 for a set of pin gauges; it's a lot cheaper than a new FAL receiver, and a whole lot cheaper than an ER visit. Besides that, having the set of pin gauges allows you to know what range of locking shoulder sizes will work for you: not every size LS is going to be immediately (or cheaply) available.