The way I am looking at my Tav right now, designed to use Great Weapon Fighting and in Heavy Armour
DEX 8 means STR 16 and taking Heavy Weapon Master as first feat.
DEX 10 means STR 15 and taking Heavy Armour Master as first feat, Heavy Weapon Master as 2nd.
If DEX 8 and 10 both suck, only DEX 14 and above (12 enough?) giving any real benefits, then maybe take DEX 8 and look out for DEX/Initiative boosting items?
How? Where exactly are you spending the rest of the stats?
You can easily start with 17 str, 15 dex, 16 con if you dump the caster stats.