You cannot do discreet 3.1 with a traditional Integrated Amplifier. An integrated amp does not have the processing necessary to decode discreet/separate HT signal. A traditional integrated amp also does not have 3 channels of amplification to meet your needs for a 3.1 setup.
You are going to need to re-evaluate your criteria. Considering you want 3.1 channels, and you want HDMI and 4K video pass-through, you are likely going to need to stick with a high quality HT Receiver, or an HT Processor and 3 channel amp (or 3 channels of identical amplification).
You are going to need to re-evaluate your criteria. Considering you want 3.1 channels, and you want HDMI and 4K video pass-through, you are likely going to need to stick with a high quality HT Receiver, or an HT Processor and 3 channel amp (or 3 channels of identical amplification).