This conversion is actually fairly popular and has been done many times in the past.
Originally a 40 S&W Large Frame AMT Backup, subsequently rechambered in 10mm Auto.
It runs fine from standard 45 ACP Backup magazines.  It's pretty snappy to shoot, but not really painful.

Tony

Thanks for sharing Tony!  Awesome conversion to 10mm!   

That is a nice little pistol.  Not real pretty but looks aren't everything.

I have quite a few AMT's and as most of you know, quality is a bit sketchy.  The Automag line pretty much never works out of the box, the little .380's are hit and miss, the 22 Magnum autos almost never function without work, but the large frame backups, have always worked for me.  I think I have 6 of them or so and every one works every time.  I don't recall ever having a stoppage with a large frame Backup.....but they still kinda suck.  The trigger pull is about 40 pounds and pretty much no sights on them.

Tony

My brother had one many years ago. Never could get it to function reliably. Yours however looks awesome! Never thought of one in 10mm.

Wow, there is one a lot like that for sale on Bunsmoker.   
Even the name of the seller is similar.   

FWIW, there is another Back up 40sw on there too....   

That is an "interesting"  conversion....can't imagine touching off a BB Outdoorsman load in one...

I've got one in .38 Super and it has run like a top...

Bob

I have always had my eye out for one of these in 40S&W specifically to do a 10mm conversion.  Nice looking gun.

Now that is cool! I used to have an AMT Backup in .45 ACP. For such a small handgun the recoil wasn't bad at all with .45 ACP. I didn't like that simple "sight channel" instead of real sights. But, it was OK for short distances like 15 ft., which is adequate for the purpose of having a backup gun. Mine was reliable and I wish that I had kept it. 10mm for a backup gun would be great!