Side mirror adhesive

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Hello everybody and thanks in advance for any input.
My driverside door mirror glass has become detached from its plastic (?composite) backing plate inside the housing. I want like to reattach it, but was concerned about 1) which adhesive and prep for a lasting bond, and 2) since the mirror is heated and the old adhesive seems to have been a very thin continuous sheet, presumedly to maintain even thermal conductivity so the mirror defroster will work evenly, how do I best obtain this uniform coating?
It seems that regular mirror adhesive would be too strong, too fast setting, would require several packs to cover the whole back of the mirror / backing plate, and likely would pool into a mess if several cc's were applied to the vertical surface. And the backing plate has a couple of tiny ripples in its smooth surface, so at least a tiny amount of thickness of the adhesive will be necessary to get uniform adhesion & heat conductivity.

I am sure I can "wing" this very minor repair, just wondering if there is a "right" way to do it.

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I’ve got an extra mirror (glass only) you can have for cost of shipping. I’ll check it tomorrow to ensure it’s solid and the heater isn’t shorted.

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Thank you Chris, that is a generous offer, but I luckily have the mirror glass itself, and in good condition. I just need to readhere it to its substrate / backing plate. I think when one buys a replacement mirror, it is probably already attached to the plate.
I didn't try to remove the backing plate from the housing b/c I thought it would likely be brittle, but perhaps that will be necessary to best readhere the glass to it. I am hoping someone out there has done this before and will comment on their experience.
If it cannot be reattached, I may take you up on your kind offer Chris.