What Simple Checks Can I Do To Detect Fake Morgans ?

Unfortunately, I don't have right equipment for that.

I tried using a digital balance with good Victorian silver coins and the results were nonsensical.

Pertinax - dependable, pocket size digital jeweler's scales can be purchased for under $20. Most are accurate to 1/10 gram, which would suffice for checking silver dollars. Very cheap insurance. One should also diligently study known genuine examples to get a better perception of what flow lines and detail should look like. Most counterfeit silver dollars that have been made to attempt to deceive collectors are crude castings, but even even 1:1 transfer die struck counterfeits will typically have substandard (mushy)lettering and devices. All this must be taken into consideration above and beyond weight and dimension measurements. Often even a quick examination of the reeded edge will be beneficial, as Mint struck coins will be very uniform, as compared to counterfeits.
Just by the very fact that you have indicated a large quantity of these have appeared in a dealer's shop in the U.K. is cause for suspicion.