Do I Have the Wrong Cartridge?

In a nutshell, your phono stage doesn't have enough headroom for your high output MM. Your cartridge is minimal, the phono stage inadequate for your dynamic classical recordings. Perhaps go back to a lower output quality cartridge, I'd say. Or, a better phono stage.
Try one courtesy of your dealer or get a new dealer.

The Rega is a very high output cartridge, but if it was overloading the phono stage it would do so on the rock recordings just as easily if not moreso than the classical records. The same goes for issues of gain and capacitance settings. Other Rega user do not mention a long break-in period.

The Rega is designed for Rega tonearms with a three point attachment method. That geometry is designed to minimize end of record distortion at the expense of higher distortion level over the entire disc side. It is possible that this distortion would more noticeable on classical recordings. Talk to your dealer about what geometry they used to align the cartridge. It is something of a longshot, but it might point you in the right direction.

Zavato, I set VTF on my Axis with a ruler and it is horizontal to platter; I was told this is correct position.
As far as my REFERENCE Classical, I'm using analogue mastered LPs from 60s and 70s...Decca, Philips, DG, and you are quite right, the digitally mastered vinyl does sound lean with very crisp highs.

Truman...Very interesting. The output specs on the Rega are 6.8 - 7.2mV. Do u know what range is a better match for my phono stage. It would be cheaper to buy a new cart rather than a phono stage upgrade.

And many thanks.

45 dB of gain in the phono stage is a HUGE amount of gain for typical moving magnet cartridges, let alone one that outputs 6.8-7.2 mV. It's no wonder it sounds harsh and strident.

With that amount of gain I'd be looking to drop the output on the cartridge way down into the 2-2.5 mV range. So high output MC's such as the Denon DL 110 and Dynavector 10 x 5 would be appropriate. The Dyna would be pricey but the DL 110 would come in way under budget and both should match up reasonably well with the arm.

Do you have the wrong cartridge? Yes.

I see these kind of posts often regarding the Elys and it reminds me of when i first moved up from a Technics auto linear tracker in the late 90s to what i considered my first quality turntable when i bought a Rega Planer 2. I asked the dealer to fit an Elys cartridge as it sat in the middle of their range and thought it would be ideal as a starter. I found nothing to recommend the Elys apart from its prodigious output which meant it would go loud and it wasn't until i moved on to other cartridges that i realised how poor the Elys is. I'm no Rega hater. I loved the Planer 2 and kept it for nigh on 12 years, buying a P25 along the way but i've never heard a Rega cartridge that impressed.

Significantly better on the Planer 2 was Denon DL160, better again was a DL304. A Nagoaka MP11 outperformed the Elys in every way as did a Goldring 1012gx and a Garrot Brothers P77.

Like many others i also bought a Rega cartridge because of the ease of the 3 screw alignment. The cartridge was a poor tracker though until i bought the HIFi News test record and using their alignment protractors with the test record found that the cartridge needed to be a couple of millimetres forward to get the overhang and hence alignment correct so the 3 screw set up was no help in the scheme of things.

My suggestion would be to try another cartridge from another manufacturer, there is plenty of choice in the same price bracket.