I think Jorah said it perfectly.I'm a newbie soap maker, but I think I know a bit about that feeling you describe of needing to rinse until you don't feel 'slimy' any longer. I can tell you that it's unlikely 'soap scum' or 'soap residue' you're feeling but the 'un-soapified' oils (when soap is made, oils are converted to soap, but it's possible to have a small percentage remain un-converted, and that leftover bit is called 'superfat,' and is likely what you're feeling).
Many soap users are looking for a bit of smoothness to prevent drying, but your preference is 'squeaky clean,' so I'd suggest finding soaps with lower 'leftover oil,' as others have said here... You may want to see if someone can make a batch for you with low superfat (zero to 2%) that you can try out.
Alternatively, buy an immersion blender and try a small batch yourself! You might find the exact sweet spot for you! Perhaps a coconut & palm oil combo that others would find too dry would be perfect for you (this is why the 'perfect' bar of soap doesn't exist... people are looking for different qualities!).
Since starting to make my own soap, and buying handmade soap from others for the first time, I've had to force myself to stop scrubbing until the slippery feeling is entirely gone... and I think my skin is starting to be less dry! (something I really needed)