But you guys have both been on the diet a while, and in OWL you're supposed to up the daily carb intake slightly each week until you stop losing so that you can find your CCL... so *technically* you're still following the diet to the letter! If you both still have a loss this week, then you'll have found out that your CCL is actually higher than 20g and you can continue to eat, say, 25g (maybe more) a day as long as you're still losing! It's certainly not cheating to up your carb intake a bit.
Staying on Induction for a long time is okay if you're still enjoying the diet, but I'd say that if you're struggling or feeling deprived it's worth switching to OWL so that you don't get totally fed up and quit. You'll still lose in OWL if you do it right, just maybe not as fast.