Terrific! Although my first instinct would have been for Clark to confess to Lois, your way is better and more natural! After all trust is a 2-way street. With Lois being so suspicious and careful, plus a TV reporter looking for a way to broadcast the story, Clark has to be more careful than ever. (It's clear Clark's been surreptitiously following Lois around so he knows exactly what she's been talking with Susan, etc.)
In one way, she's right.. Clark's powers would be the biggest proof.
Loved the little insights into their characters... Lois' combat training.. her troubles with her name, Clark's cleaning-when-nervous... plus the double games both of them are playing with each other.. superb!!!
One more thing... we know that Lois atleast knows about the Lois&Clark TV series... maybe she even has it as a keepsake of her parents & Lucy.. so how about.. after she's accepted the parallel worlds theory or maybe before it, she thinks, "hey this person looks more like the Clark in the TV series"... and maybe shows the tape / DVD to Clark or something. Or.. Clark while watching can remark, "hey Lois, this actress resembles you .. a lot"
