When you say "we know", that's opinion not fact.

Why is it assumed Howdah pistols were "shortened long arm shotguns and rifles"?

I would be pretty sure they were made for the purpose. Or similar purposes to Howdah saddle use.

The Maharajah market was a lucrative market.

We might look a modifying long arms today as the Maharajah and Brit Officer, Senior Administrator Elephant Howdah hunting market today is non existent.

With the success of Rigby and other makers, I wonder if a Brit gunmaker designed and built an authentic Howdah pistol,hammers, rifled barrels, reasonable regulation, good cartridge chambering .500 or .577. I wonder how it would sell to the "must have" enthusiast market? Would not be cheap.

Howdah handguns suffer from being handguns. In the UK, illegal no domestic market. Large bore handguns can be a problem in some jurisdictions. "Sawn off" comparisons might be a problem in some places.

Practical uses are another market issue. Target shooting. Howdah competitions. Bear defence? Follow up secondary weapon on leopard, lion, other dangerous game? A 440 gr .500 or a 480 gr .577 or thereabouts must be quite effective at very close emergency range. But also a must have for every well heeled collector. A handfull a year would be enough at the prices no doubt required

What cartridges? If looking at a specialised design I'd go rimmed. Shorten a .500 NE and a 577 NE to a "Howdah pistol cartridge" length.

Lead bullets or jacketed? Some commercial jacketed projectiles do exist.