Yes, as I said in my above post they have discounted the "soccer ball universe" (dodecahedral space) as the fundamental domain seems too large to allow it. They have not so far been able to totally discount other non-trivial topologies.
My original point was that it seems to me if it were up to you they shouldn't have even been following up possible evidence of the dodecahedral model as you deem that model implausible and preposterous and I am wondering if that is good science or not.
That paper also states that they have only found space to be within 2% of being flat, so there may indeed be large scale curvature but the radius of that curvature would be larger than our observable universe.
The paper below may interest you - it examines and
eliminates some other non-trivial topologies but concludes that although we still have no evidence for a non-trivial topology, we still cannot discount it. However, the best fit to the data is the flat, simply-connected Lambda-CDM model.
Imprints of spherical non-trivial topologies on the CMB