I have learned something that may be helpful for you.... It s not so important that your palm be able to fit into the pocket that people (like myself with smaller hands) are able to fit into between the fingers and palm of your strong hand on the grip... The functionality of this type of grip that you are employing relies on two elements for controlling recoil. When your pistol recoils there are two spots on the gun where the energy is located. One of them is at the top of the arch of the beavertail and the other is low front on the grip. Get the webbing of your support hand as high up on the beavertail as possible and grip it like you mean it. The job of your support hand is to control the recoil pivot point at the front of the grip, and this is done primarily by your middle finger and ring finger, because those fingers are are able to generate much more force than your pinky. Do you would place your support hand on the firearm with your index finger just under the trigger guard allowing you to exert force with our with your middle and ring finger (keep the tension up with your index finger also mind you), again you are going grip it and get a good pull like you really mean it.... The only job your thumbs have is to stay out of the way :)
As far as your new backstrap is concerned give it a shot you may like or may not, play around with both for a bit and I suspect you will quickly decide which one you like the best..