Thanks for the reply Henry. Everything works except the last step; the selected "edge-on" object doesn't re-orientate.
I've attached 2 drawings: "Mont2" is the source drawing for the shapes (pink) which I'm trying to copy and paste into the "Mont-laser" drawing.
I'm sure there's an easy solution. Thanks again, Jamie
There is. It's a tad unconventional, because the objects you're copy-and-pasting are a little unconventional: Groups which contain other Groups as well as 2D primitives. After fiddling with your drawings for a while, the easiest way I found to put everything flat on the Workplane is to use Assemble by 3 Points. Here's how: In the target drawing, Switch to an Isometric view before proceeding further, so you can see what you're doing. Turn on "Vertex" running Snap mode. In the source drawing, select an object and press Ctlr+C to copy it, then go to the target drawing and press Ctrl+V to paste it.
Activate "Assemble by 3 Points" (an icon in the Drawing Tools toolbar) and follow the instructions at the bottom left of your screen. When they tell you to "Select an entity whose position you wish to change," click on the newly-pasted object (I'll call it Sam for convenience). Next step is to "Specify the location of the source point." Click someplace on the edge of Sam, preferably a corner at one end. In response to "Specify the location of the destination point," click on the cyan-colored object that I see is already on the Workplane in the target drawing (click a point that corresponds approximately to the point you already clicked on Sam; it need not correspond exactly). Continuing to follow the instructions, you'll have two more source points to designate and two more destination points. The instant you click the final destination point, Sam will flop onto the Workplane. You'll still have to move him into whatever final position is required.
If time permits, you may want to clean up the target drawing by redrawing the imported objects as Polylines and deleting the messy Groups. Save the drawing under a new name first, so you'll still have Mont-laser.tcw intact in case something goes sour.