First, don't get too excited about the thermal capabilities of conductive epoxy. An epoxy like DuPont CB-100 increases the amount of heat conducted through the barrel, but many over estimate what it can do.
Calculations show for a 0.020" drilled hole with 0.001" copper barrel thickness, adding CB-100 increases the amount of heat by less than 5%. The reason is the CB-100 has a thermal conductivity of 5.23 W/mK versus 395 W/mK for copper. Even though CB-100 makes up the majority of the cross sectional area, it only adds a little to the "thermal" cross section.
Second, in response to one part of your question, we manufacturing types want you to keep via plugs at or just barely below the surface of the solder mask. If you allow epoxy above that level, it will affect the amount of solder on SMT components.
Finally, in response to the other part of your question, epoxy has poor adhesion to tin and its alloys.
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