Minimum driven head thickness .038 per Mil Spec. That's a lot thinner than what you get with the 1.5D rule of thumb for the shop head. For reference that is very thin- less than a #60 drill bit. Source: https://www.vansaircraft.com/public/Specs.htm
. So you're probably ok.
For tight rivets look up the indirect back rivet technique video on EAA's website. That might not even work for this spot though- I used pull rivets.