So I have seen many people on the forum grow their figs really close in hedges.  Some have said they plant their trees as close as 4 ft apart.  How does this affect fruiting and yields?  I am more interested in yields and quality fruit than anything but I like others have a limited (but still large) area to grow my figs.

The extra pruning required for that spacing will delay the crop. It is tempting to plant all of your trees out like that to treat them equally but the only ones that will probably succeed and be productive in your climate in those conditions are early ripening/precocious varieties. You can do it, but keep in mind it will be a trial to see which varieties are suitable for that growing style in your climate. Maybe dig up the ones that you find are not able to produce reliably after heavy pruning before frost and pot them?