The power cord to your amp will likely have a large impact. Given what you are attempting, I recommend trying an AudioQuest Hurricane. I would borrow or rent. These have become extremely popular because of their ability to add transparency and detail without negative impact of the bass of changing the tonal balance. They had a huge impact in my system.
A power conditioner is going to be more challenging for you with an integrated. Almost all power conditioners have a negative impact on current flow… so amps are usually not plugged into the power conditioner… but straight into the wall (direct line will also help). But the preamp and all other components plug into the power conditioner. Without the preamp plugged into the power conditioner you will not get as big a position effect from a power conditioner.
But to address your problem. Each of the things discussed will make a difference. They are additive! This is key. You may have to do all of them and slowly work step by step to get to where you want to go.
You want direct line/s
Top of the line power cord to amp
Power conditioner
You will get greater transparency through Transparent Ultra… although at greater cost. The new generation are better than older.
Careful running of cables… 90 degrees at crossing. Cable lifters.
I would pe patient… just slowly work one thing at a time and get it right. It is very likely you will get there.