I remember first seeing the, If I could would you, close in a sales training session when I commenced a central heating direct sales agent position back in the 80's.
They used a similar technique where the customer would be put on to the phone to a manager/closer and the hand over would be just as you say.
I have Mr X here and he will have the new system but only if we can give him, and here you added the feature that the customer had told you they were interested in.
If the customer didn't object when they heard how you had rephrased what they had said you knew you had it closed and you had your pen and contract ready for when they had finished the call with the manager.
At the time you felt great using the hard sell close, but now, looking back, I'm not proud of the practices we had back then. It's nice to see that you are bringing these dodgy sales techniques into the modern soft sell world of today.