A rookie with 10K, seeking advise

The problem with asking a wide open question you will get a wide open set of answers that won’t make your purchase any easier.

There’s a benefit of better power cords/cables, but for your system, $125 power cord will get you a bigger benefit than you think. 
There are many ways to go with your system but to get better sound quality, I would keep the strata and dac and replace everything else. Nobody can tell you to go the tube amp route without knowing which speaker you have, it would be foolish. If your speakers are on the inefficient side of things, you either need to go with solid state or a very expensive high powered tube amp. 
There are many speakers out in the market used in your price range that sound excellent: Revel studios 2, Revel F228be, Usher BE10, Totem, and others.

Try to attend a big audio show or visit audio stores across the country  that will have a lot different systems to listen too before making a decision.

op

good advice from @mesch - learn more, see the big picture, before spending the big money

we who are experienced at this hobby tend to gravitate towards speakers as the key improvement (assuming proper placement and room, as always) in one's equipment choices, but that being said, it would be wise for you to share your source equipment in use currently - after all it is a chain, so garbage in leads to garbage out

as a noobie at this, we should not make common assumptions w r t what you are doing, what you have other than the speakers and amp you mentioned

I would keep the Rega deck and cartridge. I would sell your speakers and integrated amp and go with the following:

proac DT8

one of the following integrated amps:
simaudio

yba

yba 2

speaker and interconnect cables from (I really like Mogami cables):
Take5

I really like these power cables (after trying more expensive ones and don't like how stiff they are):
volex

maybe replace the ps audio phono preamp with:
110lp

I have a very similar setup and love the sound. Check my system details page if you are interested. To sum up my recommendations:

• the speakers are easy to place with their downward firing port, natural sounding (great for vocals and strings) and go deeper than your current speakers
• the amps have plenty of drive in them for the proacs and are on the warm side to match well with the proacs
• I’ve tried the cable dance before and settled on Mogami products (it is what a lot of studios use). I like the 2549 for interconnects and the 3000 series for speakers. the furutech 126(g) connectors for the interconnects and nice quality bananas for the speakers. also, if you need XLR, he can make them or has them.
• I’ve heard really good things about the 110LP phono stage and I am tempted to try one myself, especially since it is so quiet, like the simaudio moon integrated recommended above.

If I were you, the first place to look would be here 

You’ve been given a number of good suggestions and a number of different directions so you most likely have a lot of thinking and research ahead before you make a decision. When you do narrow down some of the components you are interested in and are looking to the second hand market take a look at tmraudio.com. You will pay somewhat more than buying from an individual but they offer a two week trial period and if you are not satisfied you can return and pay only the round trip freight.