As for non cuban cigars to bring in. I would highly suggest either or both of 2 manufacturers.
My Father Cigars (or a brand they also produce - Tatuaje)
Casa Fernandez (or the brands they also produce - Warped, Illusione)
Both manufacturers bunch their cigars in the traditional Cuban method of entubado and grow the majority of their tobacco from traditional cuban seeds.
The Casa Fernandez "flavor" is more easier to decipher among the MANY brands they make. Whereas My Father/Tatuaje have more variation to their MANY brands.
Therefore I would suggest any Casa Fernandez made cigar with a natural wrapper (not Maduro or Connecticut Shade) be paired with an H. Upmann cuban cigar. (Shortbread, doughy, toasty I have found in Casa Fernandez.)
Naming all the specific cigars would take up too much space so if you're interested let me know and I can provide specific recommendations.