There's a few things that don't make sense to me in this. So your factory speakers are only able to reach 20 before distortion and the range is 40? that's a bit strange, usually you get to at least 3/4 before that. Another thing is that with your line out converter choice, there's options on the side of it. Are you sure that's set up correctly? You should never have to max your gain on an amplifier, you're running huge risk of feedback loops if you do that. The signal should be stronger than it is. Are you sure you've adjusted the gain and plugged into the right set? There are more than one gain settings for multiple channels on there.
Beyond all that, this LOC isn't the best choice for your system. Ideally you'd get a new head unit and run RCAs from that, but since you're using stock the best option is an LOC that has bass differentials so your factory unit isn't robbing the amplifier of bass as the volume goes up. An LOC like this would be much better and you'd notice an improvement regardless of your problem here.
2-channel line output converter for adding amps to your factory system
If you want to maintain the fader if you ever get a 4 channel amp to go with that mono amp then you could get this instead.
6-channel line output converter with bass restoration — adds aftermarket subs and amps to a factory system
When i switched vehicles to one that didn't give me the option of easily swapping the head unit I used a passive LOC like that one and it was pretty lackluster. Upgrading to the LC2i brought the quality back from my old car and I no longer had issues with bass levels weakening with volume.