I also have the Laney L5S running into a 1x12. It is such a great sounding amp! It sounds like a big amp without being loud and it is very responsive. I also have a modeler, the Hotone Ampero 2 Stomp (similar to the MX5), which I mostly use for effects. Finally I use the effect send of the Laney into a Baby Boom 30 watt amp powering a 2x12 cab. Getting the best sounds of my life with this setup.Funny to read this, I've had a Katana 100 1st gen, and a Yamaha THR10C and both have moved on. I don't like using the PC to tweak things either. Now I have a Laney L5 Studio (2-channel tube amp with built in XLR and USB for recording) and a Headrush MX-5 (which is a modeler but they don't even offer a PC editor). I almost think you might want something way simpler. My bedroom rig uses a Hotone Mojo Diamond but I don't know what using phones sounds like.
For low volume mostly clean playing, I don't plug in at all.