Nice bag!
I've posted the link below many times but it is the only example I have of giving a bath to a lined, pebbled leather Sheridan bag. It was a Sheridan Glenwood and it was in bad shape but it came out well.
I was new to rehabbing when I worked on the Glenwood and I was cautious, since then I have dunked many lined bags and most of them were successful rehabs.
I was afraid to use a creamy or thick conditioner on a pebbled bag back then, but now I would use Leather CPR first and Black Rock's later to try and minimize the stain. I would apply these conditioners sparingly and wipe them off quickly. You can always apply another coat of conditioner later.
Good luck and let us know how it comes out!
https://forum.purseblog.com/threads/what-happens-when-you-dunk-a-bag-that-shouldnt-get-wet.689911/
katev - Thank you SO MUCH for linking me to this thread! I will give it a bath for sure, with this encouragement, and follow with CPR and blackrocks. Do you think I should try and "pretreat" the stain by trying to draw it out with cornstarch? Or just go straight to bath and see what's what? Thanks again!