Just going over the original post, several thoughts come to mind that may not have been addressed by the excellent responders so far.

cbutts   mentions 2G cover passes are the primary undercut conditions...  

Ok, some pictures of some actual weld profiles would go a long way to determining root cause.....  Because as mentioned already, how to repair the undercut is of much less importance when compared to how the undercut is getting there in the first place.

Rework, even when the part is still on the factory floor is typically a 5X cost increase...  !!!!!

Do you want Johnny welding on base plates and stiffeners or do you want him grinding undercut or adding extra weld passes to cover undercut ?  

How many manhours annually do you spend repairing undercut ?     How many field service claims related to bad welds are you paying backcharges for ?       Put those costs against the cost of a little training and increased supervision on the shop floor ….  Training of MANAGERS  not welders...   The welders will do what they are told..  

This is a management problem not a welding problem....  Get that straight  8: O'clock Day 1.

Back to the 2G Horizontal cover pass...…..   No matter if GMAW, MCAW, FCAW or SMAW,,,, Gravity plays the biggest role in undercut, technique comes a close second.   

Are the welders trying to weave a second pass horizontally over a first pass?   Are they placing stringers?    A look at the welds themselves and the undercut is going to say a lot about root cause...… Prolly everything needed to provide a solution.

I won't rule out overheated base metal, but I give that phenomena absolute last place on root causes for undercut.   A 300 Amp horizontal stringer bead with GMAW or FCAW can be place on a 500F weldment without undercut if the technique is correct...    Unless it's glowing red, this is not likely the primary cause...  With all due respect to my betters who have already spoken to this.

cbutts
I feel for ya with the two opposing shifts.....BTDT. I used to get the ole "first shift left this for me"...."this was waiting here for me to fix when I came in this morning"....and various versions of the same blame game. I felt the best thing that happened was when we eliminated the production welding on 2nd shift, man did that free up a lot of repair work. I understand that you have a second shift and now have to figure out a course of action to get the undercut under control.

Lawrence we used a 3/32" FCAW and it was pretty brutal trying to weld the second side of 1/4" and 5/16" thick material without a few minutes in between passes and keep it undercut free.

Scott, I have seen that too. Shear tabs have given  our shop fits until I suggested that we weld the fillet weld on one side and move on to the next shear tab and then the next and so on, then come back and place the fillet weld on the otherside. This gave the shear tab time to cool off a bit and made placing the fillet weld on the other side manageable.