I do not use lightroom but if you use lightroon and change image exposure from one to to an others that seem like it destroys the whole practice of keeping all image the same so they can be stitched together the best they can so the seam will have great detail and look seamless.
I also do not believe what you see in Photomerge dialog are templates they are more like what type of Panoramic projection to create. Where Auto most like looks at the number of images, their overlap layout and the Len used to choose which type would be best Perspective, Cylindrical or Spherical. I never understood what Collage is its lcon looks just like the Cylindrical's icon without the blue background. Perhaps that is what you should use the missing blue in the icon may mean Photomerge will not try to adjust the image it will just to stitch them. When overlap is not good you try Reposition. There are additional option in the Photomerge for using additional image adjustments.
IMO When you use Photomerge you should not adjust the images used you should let Photomerge do its thing.
With two image you may want to use Cylindrical all the time with Auto either Perspective or Cylindrical will be used depend what the field of vile works out to be above 120 degrees Perspective will introduce to much distortion .
Im not individually changing exposure on single images. What I was trying to do is have the same output in alignment, of the same set of images with different exposures if possible.
In that case why not simply stitch once dupe the stitched image, Make the two layers into a smart object layer and adjust the smart object layer with Photoshop's ACR filter. as a smart filter.
Photo Merge says it cant merge smart objects. Is that what you meant?
No. You use Photomerge to stitch your un- adjusted image files into as stitch panorama document and save your panorama document. Panorama document you duplicate into a new document and target the two layer and convert them into a smart object layer. Your un-adjusted panorama is now a single smart object layer. You the use menu Filter>Camera Raw Filter and adjust the exposure of the panorama. You do not stitch twice you adjust the exposure of the stitched panorama.
I do not use lightroom but withe Photoshop I can open all the image to be stitched inot Photoshop Plug-in ACR and select all the thumbnails in ACR dialog and hasb ACR stitch the images int a DNG file I can open as a smart object layer.
It worked!! Thank you. I tried making two panos in ACR as you showed following.
"I do not use lightroom but withe Photoshop I can open all the image to be stitched inot Photoshop Plug-in ACR and select all the thumbnails in ACR dialog and hasb ACR stitch the images int a DNG file I can open as a smart object layer."
After making adjustment before creating the second pano, it was processed with the exactly the same stitching. When I did this with Photo Merge directly or through LR, the shape of the output pano was slightly different. It's as if different control points had been selected on the lightened image.