I have another suggestion that will probably work pretty well, as long as you are not using this foil-lined tube as a "stuffer" (the length of the tube only being 2.75" for a "D" engine or 3.75" for an "E".)
Assemble your motor mount relatively standard, except put the forward tab of the engine hook over the forward end of the engine tube, rather than the standard method of piercing the tube and inserting that forward tab of the engine hook through the tube. Secure the hook to the engine tube on the outside using heavy duty tape or a some other method. You will need to trim about 1/4" off of the thrust end of the motor tube doing this so that the engine will protrude from the rear of the tube enough for you to grab it and remove it after flight.
Anyway, after your mount is completely assembled, get a third centering ring that will fit the tube you're putting this mount in, but use one that centers a BT20 in that tube. For example: If you are going to put this mount in a BT60, this third centering ring will be a CR2060. Now, glue this centering ring into the body tube of your rocket at the location that will be right at the forward end of your engine tube. Then glue your motor mount in right up against that CR2060 (in this example.)
The third centering ring for the BT20 will be of smaller diameter than the inside of your heavy duty BT50, and if installed this way, will effectively act as a thrust ring for your motor (although this "thrust ring" will be glued to your airframe tube and not the standard method of being glued to your motor tube.)
I have attached a sketch of what I'm describing, maybe that will provide more clarity. Hope this helps!