Sub-frame connectors... Please build them correctly!

Do frame connectors add torsional rigidity - Absolutely!

Jack a car up from the front corner and see how high it lifts before the pass side tire leaves the ground. Put on connectors and do the same. The height will be reduced.

Do the same jacking it up the trans x member and see how high it needs to go before the rear tire comes off the ground.

Using the floor pan as a sheer plane is OK. Put lots of power to it and you may end up tearing the floor pan. Mount a rollbar to the connectors with the other points of attachement and this is mostly a moot point