A 20ga chamber should taper from about .700" just ahead of the rim down to about .685" just where the forcing cone begins. I don't know how you are measuring but somehow doubt your caliper readings. If the chambers are indeed .670" they weren't finished, & I'm surprised you can even get a shell in. The pins look too pointed & perhaps too long as well, primer indents are certainly deep enough. I also suspect the timing of your cocking levers is off & hammers are not beginning to cock on initial opening of the gun.
