We all know that whenever possible, we want thermal relief between the barrel/pad and the copper foil to make it easier to properly solder that through hole connector.

My question is, assuming there is no connection from the barrel to a copper layer (or in this case, 4 sheets of copper that aren't connected to it) but the gap is narrow, is there any reason to think that expanding that gap would provide any additional thermal relief? Does heat flow jump a narrow gap easily enough that additional relief might be of some benefit?

Edited to add that the barrels that we're having problems soldering to have a 4 mil gap between them and the copper layers they not connected to. The other two have 10 mil gaps and no issues, hence the question.

The balance between scorching the board and 50% top side fill is touchy with this one.