Is your image centred?

Your variations from track to track point to cartridge alignment issues, you should have very little variation within a single LP. I suggest if you're going to keep your present turntable for some time, get the MintLp Tractor alignment device, about $100, your deck will sound a lot better. I found it better than VPI alignment jig and DB protractor. Just google MintLp tractor.

Luna, changing the interface to your table and hearing improvements does make a lot of sense. Different materials resonate in different ways and can sometimes smear the notes causing all kinds of havoc. I've been through that with hard maple, granite, Stillpoints, etc. All tables are different so it does quite often require experimentation. For me, about 1/2" of aluminum as a shelf has so far worked the best with my table.

I have made some improvements again! It is the null point there was out! I found the template and reset the arm. The overhang may be out but I can’t do anything. The two albums that I listened last night were centred, not shifting around as I remembered. Just a little distorted at the last track. May need to fine tune something else?
I am getting excited!
One thing I noticed is that the sound stage has grown much wider. There is much more spatial information coming from the speakers. More music fidelity means more to worry!!!...Just joking, I am enjoying all the way. Will up-date again.

Thanks all for your input.
To sum up, I have successfully revived my 20 years old turntable. Amazing that it stands its ground against a top CD player. The most useful tweaks in my situation are azimuth setting and a very solid platform underneath the turntable. Interestingly, I found levelling of the platter not very important as it is impossible to have it and the arm base level at the same time! The inner and outer grooves are not levelling too!
Now, the image is dead centred with good recordings. With not so good recordings, the centre image will floats left or right but the background music is coming from both speakers. Where as in the past, all the sound seems to have moved to one side of the speakers only.
Have a good analogue session, everyone.