I have a classic LP12 & I don't think the Ittok is a weak link compared to a RP6 as you seem to sense it.
So, like others have indicated I don't think an RP6 can be a step ahead.
With the classic LP12, there's 3 things that absolutely make sense in my opinion:
1) Have the arm bearings checked and fine adjusted, the armwire changed by Audio Origami.
The original armwire (incl.the external) is an absolute no-go in my opinion.
Then you hear your arm first time what it really is capable of, the difference is not subtle.
2) Get a Sole subchassis by Analogue Innovation, or any other aftermarket solution for sensible money you like.
I only have and know the Sole, so can confirm this is great and transforms the performance.
The original steel subchassis is seriously holding back what a classic LP12 can do, a circus kit however, in my opinion is not necessary, contrary to common wisdom ,
if your original bearing is ok, means, has no pitting.
Don't get persuaded into a circus kit if your's are ok, the difference is not really breathtaking in my opinion if you recognise it at all.
The subchassis makes a huge difference, though..
3) possibly build or buy s/h an external power supply, not a Lingo
I think this is worthwile, still have a Lingo myself but I heard and preferred others, i.e. Norton among others.
That's the imo sensible things you can do with a classic LP12, won't cost a fortune & is in my opinion good fun doing and enjoying the results.
Maybe you are satisfied and fine with that, depends on the music you hear, what you expect from your deck..
If you want more than this, the LP12 won't get you any further at this point.
Not for reasonable cost in my opinion.
If you want better than this, you'd likely spend ~3K upwards, perhaps with a few exceptions below that at good s/h opportunitys.
Personally, I would look onto the Well Tempered Amadeus the moment,
maybe listen to a Funk Vector and a Rega P10 among others
and compare to a simple, but keeled LP12 , preferably with an affordable system on.
If you like what the LP12 does, start doing your's as above.
If you prefer one of the others clearly, leave the LP12 at this point & get another deck.
Sell the LP12, or..just keep it as it is.
..and Mull is right...take your time, don't rush it.
The deck you get should be more satisfying overall, in every aspect,
otherwise you'd risk turnring in circles & you prefer some music on deck A and some other music on deck B..