What is the model of your Sharp Aquos TV? Since your TV seems to support the discrete input selection method (Method 2), then concentrate on it.

Try all the discrete input commands in device mode. Make sure their action is discrete and not toggling or cycling. If they don't work properly, then re-learn them from the original remote. Learn them in RAW mode if necessary. The RAW mode option becomes available after selecting "custom" at the bottom of the learning page.

If the discrete input commands work properly in device mode, then make sure the "Adjust Input" Method 2 configuration is using the same command names (not label names) that worked in device mode.

If the discrete commands work properly in device mode, AND the Adjust Input is configured properly, then try increasing both the inter-device and inter-key delays.