I've never shot a tiger, bear or lion at all. Let alone with a shotgun slug or ball.

But I think a 10-bore or 12-bore shotgun, in the short 16 to 20 inch "coach" gun pattern, preferably with hammers, loaded with ball, slug, brennecke etc perhaps with rifle sights(?), or sans a rear sight, flip (?), would make a good Howdah defensive long arm.

Why preferably with hammers? Any of these pistols, or long arms if continually having loaded chambers, it would be much safer with hammers decocked. A lot of modern doubles can benefit from a form of decocking hammers.

The knockdown effect of a 10-bore 700 gr ball at very close range should in my armchair opinion dealnwith a tiger on one's elephant's back. Or a 583 gr 12-bore.

If a 12-bore with slugs can deal with brown bears, it will handle a tiger or lion.

With decent flip up rear sight, and decent ball regulation, might make a decent closer range medium game or big game hunting firearm. Certainly the 10-bore double rifle long arm fulfilled this hunting role.