(37,850 *.727)+37,850 = 65366.95 mg of CaCl2+2H2O

or a total of 65.37 grams of calcium Chloride Dihydrate into 1 liter of water

Something is wrong here. (37,850 *.727)+37,850 part doesn't make sense. You know calcium is 0.273 (27.3%) of the salt mass, so you need 37,850/0.273 = 138,645 mg or 138 g.

If so then I just need to know how much a level tsp of CaCl2+2H2O weighs?

Yes.

I thought perhaps the molar weight numbers would help predict the volume

Unfortunately - no way. Tables and MSDS.

I found this on an MSDS sheet

Specific Gravity: Bulk density: 0.835 (Water = 1)

I do not know what to do with this info

0.835 g/mL - bulk density is also called "apparent powder density", it takes air between crystals into consideration.

Density: 1.85g/cm3(20ºC)

1.85 gram/cubic centimeter = 1.85 gram/milliliter

5 ml in a metric tsp ( 5 cubic centimeters) = 9.25 grams per tsp

No idea what density it refers to. Could be it is the density of the crystal itself, if so, using it leads nowhere (your solution will be diluted much more then you think).