I'm not super familiar with '66s.

I'll tell you what I do know about '68 to '70. The overall construction is probably close, especially judging from the pics.
I've replaced that metal on my '69 within the past year. It is a pretty big repair, to really do right and not cut corners.

On 68 to 70 there is a rear crossmember, a left and right extension at each end, and two reinforcement plates where the bumper brackets bolt through.

Reinforcement plates point to the rear.

The extensions are corner filler pieces and are welded to both the X member and the trunk extensions....These are lap joint spot welds, which is a very handy and perfect place for rust to start.

The frame rails and leaf spring mounts all have tabs that the bumper bolts go through +the crossmember+the reinforcement plates.
These three layers are lapped together and spot welded, another great and perfect place for rust to start.

First thing I would do is attempt to research how different a 68 to 70 is. If there is a chance you can use a reproduction crossmember/extensions from a 69
with minor changes, I would do that as a labor saving tactic,....existing stuff can be cut out and new stuff welded in. Frame tabs are pretty easy to fabricate. The crossmember is just a piece of U-channel but has additional stampings that would be time consuming to duplicate. Gas tank strap slots may need relocated and other work may be needed for it to be useable on a '66, or it may not work at all...but it would be easier to rework a new part rather than an old one.

If the pieces that are there must be repaired and no reproduction parts from other years can be used, then you are looking at cleaning all the undercoat off, removing the spot welds from all parts, repairing all the rust, welding it all back together, then finish work.

Here are pix from Mark's 68 road runner build thread which you may find helpful if you'd like to compare the reproduction X member to the stock '66. You can see where he's welded it to the frame tabs. In these pics he has not yet installed the reinforcement plates, which look a little like a miniature guardrail.




Look it over very carefully, though.....On a '68 to '70 The trunk floor is also welded to the crossmember (more lap joints, more chances for rust). It's easiest to just cut out the trunk floor when doing this repair, rather than try to remove each individual spot weld. On mine I ended up replacing the entire trunk floor even though it was not in really bad shape, because it went along with the crossmember repair/labor savings+quality. The tail panel is involved with all this, also. To really do it right is a big job.