Cartridge advice

Pick up the phone, call Peter Ledermann at Soundsmith.
I would think you would be looking at an Otello
https://sound-smith.com/cartridges/fixed-coil/otello
Or maybe a Carmen
https://sound-smith.com/cartridges/fixed-coil/carmen-mk-ii
Think they are now 25% off so right in your range.

Hi dmcneilly, I was recently gifted a new VPI Traveler with an Othello. I feel it is a really good cartridge and they are currently available slightly under $400 new, (plus I'd like to support Peter right now) So I fully agree with Miller ... I know ...  some like to debate or mock Miller, hey,  lunatics belong here too! 

Get a new Sonata. Give Grado a call and they might give you a trade in discount for your older Sonata!

Get the Carmen. You won't regret the extra expense. It's just better for little additional cost. Retipping is so inexpensive that cost of ownership is less than you think.

For ’12 inch tonearm this "SP" (Special) version is a killer.
XSV/3000SP compliance is 15cu at 10Hz, and this is the only Pickering top of the line cartridge with lowered compliance for modern tonearms, the rest of them are twice as much in compliance. For $400-500 NOS it is a steal! Stereohedron diamond tip (long life for over 1000 hrs). Try vintage MM - they are the best for the money and outperform almost everything twice the price. Higher models (XSV/5000 or low impedance XLZ/4500 and XZL/7500) for lighter tonearms are even better. 

Luminaries. The word you were looking for, isochronism. 

I'm using a Carmen with the VPI Aries Scout and enjoy it greatly. I did have to purchase extra weight to add to the headshell but they are available for about $10 shipped on eBay.

Miller, you've shown me the light. 

I would want to move up to an advanced stylus shape: microline, stereohedron, shibata, sas.

many of those mentioned above are elliptical stylus, less contact surface, ....

and I stick with Moving Magnet, high enough output.
and, user replaceable stylus

new audio technica offer their ML microline shape, and now have alternate Shibata shapes. 

https://www.audio-technica.com/cgi-bin/product_search/cartridges/cartridges.pl?lang=eng

I put a new SAS stylus from Jico into my old Shure V15vxmr body.

I like the brush feature of the Shures. The Pickering recommended by Chackster has stereohedron tip and brush. The brush can be left up, play, then put it down/adjust tracking, play, hear any difference? if not, use the brush, it's a shock absorber, anti-static, duster.

Don't fret too much on stylus type. I've a Decca with an elliptical and it blows away my AT750 Shibata. The generator is important too. 

For the price point-$400, I have found the SS Otello a very nice performing cart on my VPI. 

I used it as a back up for my 5X  the price MC. Very nice mids, which may be address your requirements, as a Classical listener. 

The only downside is no depth charge bass performance, which isn't a Classical music necessity. The cannons on the 1812 will  just  be a little softer.

The SS website notes this deficit about the Otello.

An all around budget MC is the Audio Technica OC9. 
https://www.lpgear.com/product/ATC01.html

For the price, it may be the "best?"

The Hana SL is a very nice cart if you can stretch your budget by 50 bucks.

A couple of very nice Audio Technica cartridges come to mind. The AT33SA can fall in that budget. So can the OC9 family, there are some new members as well as the OC 9 III. If you can stretch a bit the ART-9 is reported to an excellent all around cartridge. 

Don’t fret too much on stylus type. I’ve a Decca with an elliptical and it blows away my AT750 Shibata. The generator is important too.

Your Decca does not have a cantilever at all, it’s a MI design and very special in it’s own way (the lack of cantilever is a goal of Decca), but this cartridge is not for every tonearm. Garrott brothers retipped Decca for years for their clients (with better stylus profile) and it was huge upgrade.

The problem with Decca MI and all MC cartridges is re-tip service, with simple profiles like elliptical the owner will have to re-tip every 600 hrs. With MicroRidge profile a cartridge can be used for 2000 hrs. With Stereohedron profile over 1000hrs for sure (or even longer). Profile is important anyway.

Pickering XSV-3000SP has the most advanced stylus shape called Stereohedron which is achieved by grinding four flat surface on the diamond at precise angles to each other and their intersection creates areas used to contact the groove. The advantage of the Stereohedron stylus is that because of it’s long and narrow contact surfaces it tracks high frequency modulation minimizing groove wear.

Expert Stylus & Co. in UK was Stanton/Pickering diamond supplier, they are still in business, their new profile called Paratrace. This is the best company for Pickering/Stanton service (if the owner can’t find an original spare styli). As far as i know Decca owners often re-tip their Decca cartridges with Paratrace profile in England. 

@chakster I have 2 Garrott Bros Deccas and they are excellent. I also have a Super Gold with Paratrace tip from Expert Sylus fitted by J. Wright of London.