My bad, the user manual for your receiver is shared by the RX-V773 and I mistakenly looked at the diagram for that model instead and thought yours had pre-out RCA connections. Unfortunately, the "Audio Out" RCA connections on your model are for connecting recording devices only and not for a setup like I recommended. Very sorry for my mistake.
The 3070 will definitely be a step up. Whether it'll be a big enough step to justify the price, only you can decide... but worth a shot if you buy from somewhere with a decent return policy. Another nice thing about trying it is that since the 3070 definitely does have pre-outs, you can add on an integrated amp down the road if you find yourself craving more and as budget allows instead of being at the end of the road with it.
Apologize again for steering you down the wrong road.
The 3070 will definitely be a step up. Whether it'll be a big enough step to justify the price, only you can decide... but worth a shot if you buy from somewhere with a decent return policy. Another nice thing about trying it is that since the 3070 definitely does have pre-outs, you can add on an integrated amp down the road if you find yourself craving more and as budget allows instead of being at the end of the road with it.
Apologize again for steering you down the wrong road.