The PWs are not going to eliminate finger squeak. It will reduced it nicely, but without technique, it will still be there. These are nice strings though. I use them over RWs and get good life out of them. If I need a full RW tone, I have Boomers on my pbass. PWs are not thumpy by any means, but works well with foam under the strings at the bridge for that thump. Very versatile if you don't mind foam.
I use Cobalts, TI flats, and Fender 9050L flats. I like all three but those are quite different. The Cobalts are the brightest flats I've ever had. While those are not RW tone, it can reasonably pass for it if needed.
I switched out to TI flats because I don't get decent life out of Cobalts. These don't have the highs of Cobalts but since they are very mid and high-mid centric, it can be fooling at times. Very nice strings but pricey. Some say these are too floppy, but that's more of an embellishment. Floppy is what happens to strings when one dives the tremolo. TIs are nothing like that.
I have the 9050L on my EBMM Sterling. Those are middle of the road flat wounds in between traditional like LaBelle and Cobalts. Flexibility-wise, these are the least flexible in feel of the three, but not bad at all. TIs are the most flexible feeling with the Cobalts being not that far behind.
I played Rotosound FWs for a couple of years back in the 80s and those were stiff, stiff, stiff per my recollection. These three FWs are nothing like that.
People say that Daddario makes the 9050L strings for Fender, and these are really Chromes. I don't have enough experience with Chromes to say whether those are Chromes, close to Chromes, or not. The 9050L are the smoothest of the three FWs. I don't experience finger squeak with any of the three, but our technique would make it a subjective comparison.
So with that said, this is only my experience heavily influenced by my tastes. YMMV.
If I was in your shoes, I would look at PWs if you are looking for RW sound without the bite of the highs. I use to say that PWs are RWs without the RW zing (I golf with Ping Zing irons). You'll get reduced finger squeak that should be easy to adjust and not have any.
For flats, I would go with 9050L or Cobalts depending on how much highs you want. The 9050L should be the cheapest, price-wise. So there's that.
I would not spend the money on TIs unless the OLP is your #1. The TIs are on my #1 bass which is in my avatar. Although I've been playing the EBMM Sterling for the past 4 weeks.
I back up church choirs every weekend, with rehearsals one or two days out of the week. Consistently, week in and week out. I feel that I have a wider latitude in strings than if I was playing in a cover band.