Help needed to straighten curves in panos

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I am not the best at editing and have experimented with this, but I don't get the results I am looking for. Any advice, tips or links to helpful videos would be appreciated.

I have taken several 180 degree panos of churches. Start pointing at the alter and rotate over my head until I am shooting at the door. These aren't to everyone's taste but I like 'em. Here is a recent example:

Barts&Gaetano II by Ian, on Flickr

Ignoring all the retouching needed, what I would like to be able to do is straighten the pillars and columns so that they appear to radiate from a central point. As examples, Peter Li's "Confetti" or "Veles" at https://www.plipictures.com/omniscience is what I am looking for. Peter has been super helpful with advice on shooting technique so I'd rather not annoy him with yet more questions on processing. I can get close by using the warp tool in Photoshop but columns aren't dead straight, just approximately so, and further efforts end up with too many random distortions. I've tried with puppet warp too as I thought the ability to use pins would help, but no luck.

Any thoughts appreciated.
 
Just a random thought.
Could you draw the straight lines on a new layer, and use them as a guide for warping?

These do look good, Ian (y)
 
All depends on panoramic model used. I'm guessing spherical so you may as well do full 360 and project accordingly with 360 software
I did wonder whether that would be an alternative. I usually use spherical in either Lr or Ps. From our conversations, I am pretty sure that Peter starts with this projection too, correcting the curves in Ps somehow. Again, I will investigate. Thanks for the prompt.
 
I use grid lines for anything vertical or horizontal but I don't know how to generate diagonal lines, but I will look into that, thanks.
You have to do it by hand on a transparent layer (silly colour helps), with just a very small brush size. Aim at point A hold shift, then click on point B :)
If nothing else it'll give you an edge to aim for.
 
Could you post the original images so that we can see what the distortion looks like in the original images.

Andrew HATFIELD | Architectural and Interior Photographer
I will try and dig some out. I use either a 10mm lens on a 1.5 crop body, or a 10mm on a full-frame (usually the former). Each pano is made up of 8-10 individual shots. So the first and last are usually distortion free as the camera is vertical, but the in-betweeners have heavy curvature. The shot above is a simple crop from what Lr or Ps generated as a pano. I haven't tried to straighten those curves.
 
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