Thanks for your replies!
I tried specifying the srid and "basic" coordinate precision (in case the sdelayer register command was trying to round nearby points to the same point):
sdelayer -o register -l zBldg2,shape -e na+ -t GEOMETRY -C objectid,SDE %auth -R 54 -P basic
This gave the same error "Invalid entity type (-29)", but on a minor note, it did not create a table with the same name afterward.
To keep things simple, I have only a single feature in the feature class, a closed single-part polygon -- the WKT, for example, is:
POLYGON ((-8899212.0936 4488955.4609000012, -8899222.9883 4488964.9522999972,
-8899254.6753 4488928.5802000016, -8899253.7593 4488927.7823000029,
-8899256.4052 4488924.7453000024, -8899268.3965 4488923.9197999984,
-8899271.4336 4488926.5656, -8899270.6356 4488927.4815, -8899307.0077 4488959.1684999987,
-8899316.4991 4488948.2736999989, -8899280.127 4488916.5868000016,
-8899279.3291 4488917.502700001, -8899276.292 4488914.8568999991,
-8899275.4665 4488902.8655000031, -8899266.4037 4488894.9699999988,
-8899254.4123 4488895.7955000028, -8899251.3752 4488893.1497000009,
-8899252.1732 4488892.2337, -8899215.8011 4488860.5468000025, -8899206.3097 4488871.4415000007,
-8899242.6818 4488903.1285, -8899243.4797 4488902.2126, -8899246.5168 4488904.8584000021,
-8899247.3423 4488916.8497999981, -8899244.6964 4488919.8867999986, -8899243.7805 4488919.0887999982,
-8899212.0936 4488955.4609000012))
My reasoning was that if I pulled this single shape from a good working feature class that ArcCat is already happy with (the Bldg FC that I copied the row from), it should be an easy, valid geometry to register.
I tried omitting the nil and multipart portions from the entity type:
sdelayer -o register -l Bldg2,shape -e a -t GEOMETRY -C objectid,SDE %auth
This still gives the invalid entity type error, though.
Thanks,
--John