Your rechambering to 7.62x54R will work. Had it done in San Antonio in 70 or 71. And that was on the old cast H&R Topper receiver. Reloaded with 308 bullets and it worked great. Also shot the military surp ammo. The best reason to go with this project is this is a hobby, and you do not have to explain or justify your wants to anyone. (Well, maybe to a wife!)
Furthermore, I have an opinion on the subject of rimmed cases ejecting better. Both rimmed and non-rimmed chambered Handis have the same extraction power, or lack of same. It just happens that the older rimmed cases are more tapered, therefore allowing easier extraction. Rechambering a 308 Win to 307 might add a rim, but the case will still have the less taper of the 308, therefore can experience a stuck case just as well. I've had extraction problems in 223, 243, and 308 Handis. Never in 30-30, 30-40, 45-70. Now, due to that weak extract, any chambering can have a stuck case from a hot load, dirty chamber or dirty extractor. Also a over heated barrel will stick a case. (Common when shooting all day in a P dog town.)
Several board members have reported success with polishing chambers to cure sticking cases. In these cases, it appears that NEF just did a sloppy chambering job. I personally have not done this. If have a sticker, I just consider it a POS and unload it. I have no desire to invest the time to go this route when I can buy a different rifle and spend my time at the range or hunting, rather then playing with Fitz polish. Don't get me wrong. I love my Handis when they shoot. I have a Ultra 25-06 that will out shoot both my 25-06 Remington 700 and 25-06 Browning 78. But not every Handi is going to perform like this. And at their price, we should not expect them too. They have their place in the shooting world, but, just like wine and cars, you get what you pay for. Again, just my opinion.
Good shooting..mt