I'm just going to agree with stuff already said.
I'd first pattern the Stevens-it may just be perfect for your need. I've grown out of the trap of thinking I need more/better, when i have something just fine already.
2-the 20ga is plenty for turkey at normal turkey ranges.
3- 3'' shells are not needed. Magnums are fine, but all my turkeys have been with 2 3/4'' shells.
4- If the Stevens doesn't pattern well, try multiple loads and manufactureres, then look for the sb2 receiver. Of course, you may want to search out sb2 receivers anyway, even if the Stevens works out. The handi's make great, safe, reliable rifles and with the sb2 you can buy any barrel you want to tailor your gun for any particular game species or body type/size.
5- Like dikkillr said, an auto 12ga will kick less than a handi 20. Here again, the Stevens may just be the ticket to combine a little bigger gun with the slightly lighter 20ga load.
No matter what, enjoy the process coming up and best of luck to your wife this next season