Ok. I finally figured out what I needed to do and now Splashtop Remote works wonderfully! Thanks all for the help.
Let me post my fix for anyone else who may be having issues figuring this out.
You do *not* need both a local and a remote connectoid as I first thought. Once you get the ports forwarded and the WAN IP properly listed, Splashtop will connect right away. Once I figured that out, I deleted my local connection.
Note: As a matter of convention, I normally assign static IPs to any device that will be around the house for a while. I let transient devices have the dynamic IPs I leave open on my router. I think port forwarding will pretty much require a static IP too. Or so it would appear to me since you have to list the LAN IP of the computer in the port forwarding section. If that IP changes from time to time, I think you'll lose the Splashtop connection. When I ran a test by changing the LAN IP in the port forwarding section, Splashtop reported the connection lost. So use static IPs for your computers is my suggestion. I'm not sure what to do in the event your router software won't allow static IPs as the OEM Linksys software on the WRT series initially did. Maybe Linksys has corrected that now.
I found that I had to set this up in two places. My router firmware (Tomato 1.28 on a Linksys WRT 54G v3) has a port forwarding feature. Unfortunately, I didn't know what information needed to be plugged into the various boxes and further, I didn't know where I was supposed to put my WAN IP. The Splashtop instructions merely say: "Link (associate) the ports with the home PC's IP address."
Splashtop Remote : How do I connect to my home PC from outside of home?
That's pretty cryptic.
Here's what I had to do:
1) I went to the port forwarding feature of my firmware and plugged in the port range (6783-6785) in the EXT ports box, plugged in the static LAN IP I assigned my PC (in another router page), and typed in splashtop in the remarks box. I left the Src address blank and the Int Port box blank and typed in my LAN IP address in the Int address box. The WAN IP is not needed in the port forwarding setup on the router. You need that info for the client software on the iPad.
2) Then I looked at the WAN IP address of my PC (available on my router firmware or at one of the what's my IP sites) and used that info in the client software on the iPad.
When you crank up Splashtop Remote on the iPad, it brings you to the screen that shows your computers that are available. If yours is not there, use the + button to add it. Type in the name of choice and then use the WAN IP for the IP address and press done. That should be all you need to do.
I hope someone will read this thoroughly and correct any errors I've made in my process or assumptions.