I see there's been no replies, but I can comment some, and hope my comments help you.
Firstly, I've never heard your Kenwood model, so there's that, and cannot speak to just how good, or bad the phono section is inside it?
Phono Pre-Amps today have prices all over the board, from probably $29 and up to and exceeding $20,000.
And there's a whole lot in between. There's solid state, and tube as well. Each can have their pros and cons.
Many of the solo Moving Magnet Phono Pre's aren't generally too costly. Whereas the ones for Moving Coils can be. Many of the better built MC Pre's today generally have a selection of adjustment settings in gain and loading to meet a variety of MC Cartridges available, but often they also do have provision as well for MM, (commonly MM's require 47k Ohms loading) and as well many High Output MC Cartridges can work well at 47k Ohms loading also.
It's said by some that MC's with a output of 1mv or higher can work just fine at 47k Ohms. Commonly, gain for most MM Cartridges is in the 40-50db range. And such gain might be suitable for HO MC's as well.
Many vintage pieces of gear were not all that state of the art in regards to phono pre sections, and as you can imagine, everything is built to a price point. There's so much spent here, and spent there on gear like Receivers, Integrated Amps, and Pre-Amps.
Such an example, you're not getting TOTL Magnum Dynalab or Day Sequerra Tuner build and quality in a vintage Kenwood, Sansui, Pioneer, Marantz, or even McIntosh Receiver or PreAmp.
Fast forward to current day, I might go out on a limb here a bit, and say that it's quite possible a stand alone $400-$500 MM Phono Stage could out-perform the MM Phono Stage in a brand new $5000-$7000 McIntosh PreAmp.
Thus in a nutshell, I can probably say this without getting myself into too much trouble here, is that separates can often and will likely outperform "one box" systems by leaps and bounds.
As one example, I experienced this myself 25 years ago, when I began going into separate phono stages, and was surprised that relatively inexpensive outboard Phono Stages in the $100-$200 range were quite good, and better than what I had within a couple PreAmps in use.
It's hard giving advice to any person, because everyone has different needs, has different goals, and also mainly differences in how much money they wish to invest into their audio system.
As for let's say an Integrated PreAmp and Power Amp, some might be content with vintage, and then there's other end of the spectrum, folks shelling out the cash for a state of the art piece of gear like the Gryphon Diablo 300. Heck, I'll take one! LOL
And no, not necessarily saying one has to throw money to no end to achieve pleasing audio. Such can be accomplished on a beer budget when favorably combining select pieces of equipment, and that they have good synergy.
I will refrain from making specific suggestions of a phono pre, but they are out there, research and reviews, plus other's comments might possibly help you better decide which direction you will choose to go?