NW-Bound's logic won the day, and I purchased the Harbor Freight tool, which actually gets good reviews. It only costs $3 more than the little hand saw I almost bought.
I got a few extra blades, too. It comes with a nice carrying case -- that is, the cardboard box it came it.
OK, here I am ready to go. It's great that Lena's out of town, so I can use a nice towel as a dropcloth.
The first cut was tricky (on the job training), and I found out that the circular saw attachment was much better. I could slice at the side of the divider, cutting through gradually. But the first cut was problematic:
But I got the hang of if for the second and subsequent cuts:
I cut out the top, front of each divider, which will be discarded anyway. That allowed the divider to be pulled loose from the back. Little nails were used at these attachment points, but no glue.
And here it is with all the dividers taken out:
It will be a little tempting to cut the shelf back, but I know I can tolerate some overhang.
There were three little nails holding each divider in. I opted not to drive 50 miles (RT) to buy a metal blade for cutting those. The wood blade worked OK, and I don't think it was worn down too much.
The dividers are in good shape except for the first one. The shelf got a little scratched up, but I can sand and refinish that. The next step will be to reshape the dividers, and reinstall them. The wood in the groves is removable.
That tool is nice, and I'm trying to think of other jobs I can use it for. The quality seems fine, and, big spender that I am, I've already gotten my money's worth.
Thanks for the help, guys and girls, especially Soupcxan and NW-bound and travelover, I really couldn't have done it without you.