Sure you can use alligator clips. You need to power each end opposite polarity, to simulate each end of a reverse block. The middle section will be connected to the module. So, you'll need four leads for the ends (two each) and four more for the leads of the module. Really no different than on the layout. When the first axle of the loco bridges the gap at either end, it will cause the module to change polarity in the middle section to match the end. If the module doesn't flip, its bad. No, it won't damage the sytem. At worst, if the two polarities touch , it will trip your breaker.
Your turnouts are not the source of your troubles.
Reversing loop, reversing block, reversing section, all the same as far as the module cares. You just need one. Your diagram looks fine, if the gaps are good (not bridged) then only the module can be at fault. Or perhaps, voltage drop. If the module proves good in the test, try connecting a dc power pack in place of the dcc. This because you can read dc voltage with a regular meter, you can't with dcc. Read the voltage at the point the power is connected to the rails, and at the gaps at each end of the reverse block. If there is much of a drop, the module may not work correctly.
Good luck