the sound of massed violins in classical orchestral recordings

Yeah, it just seems to be one of those things recording engineers have trouble with. I've got hundreds (thousands?) of orchestral recordings on CD, vinyl and cassette, and probably only about twenty or thirty of them get orchestral strings close to truly clean & right.  I'm picky enough on this topic to rate the various labels on their orchestral string tone cleanliness batting average.  It's one of the reasons I have so many orchestral recordings on Philips.  Analog recordings usually do better on this front than digital ones, but that doesn't mean that analog and vinyl are superior in this respect.  I also gotta say that streaming via Qobuz and Primephonic probably does better with this aspect of reproduction than any other media.  Who'd a thunk it?

I think the quality of the recording has as much to do with this as anything.  Most just do not get it right.  Occasionally they do:
Beethoven Overtures, Sir Collin Davis.  A beautiful SACD recording on the Sony label, manufactured in Japan that I am enjoying right now.

If violins sound gritty something is very wrong with your system.

As others have said, massed violins, especially playing ff, are hard to record, but some engineers and some labels seem to get it right at least some of the time.  In my experience early all-digital Deutsche Grammophonen CDs were some of the worst offenders.  Things can be ameliorated by seeking out more "forgiving" components and more "forgiving" speakers.  The problem is you may lose an incisive quality that you like on other recordings.  It's a fine balance.  The sorry truth is that you're unlikely to find mid-fi that walks that tightrope successfully.

I agree with everything that has been said previously.  Massed violins may be the hardest thing to get right.  Perhaps the next most common problem is trying to reproduce massed voices, especially sopranos, properly.  In my view these are similar problems. 

 Every single thing in the chain from the recording to your listening room has to be just right.  Therefore, it is likely you will need to address several contributors with an incremental improvement after each change.

We can do nothing about the recording quality.  What we can control is our system/power supply and room.   When the source of a problem is unclear, it usually makes sense to look into those things that are likely to be weak links in the system/room or things that are relatively inexpensive.  I probably wouldn't start by changing components.  If your car isn't running right, you probably don't switch out the engine first.  My experience is that grain/grit is most often related to power supply and/or ambient EMI/RFI.

In your system description, I didn't see anything about your power supply.   Power supply to the equipment must be addressed.   PC's, IC's, and speaker wires vary in their ability to reject ambient EMI/RFI and to present grain free high frequencies and also in the extent to which they contribute to grit and grain.   There are also products made by companies like Synergistic Research and Audio Magic that can help with reduction of ambient EMI/RFI in the listening room.  millercarbon is absolutely correct in stating that every inch of wire from the breaker box to the speaker cone can influence problems like this.  I once had a noisy duplex that was raising hades with my system until I replaced it with a good receptacle.  BTW, I've had some brand new ones that sounded just as bad, so buy an extra or two and try them all.   If your duplexes are old, get some good new hospital grade duplexes and see if that makes a difference.  I don't know that addressing power alone will get you where you want to be, but I do know that you won't get there until you have a good clean power supply. 

I've found that vacuum tubes vary considerably in their ability to render violins properly.   Not to state the obvious, but are your pins nice and clean?  Do you have back up tubes that could be evaluated?

While your statement regarding the use of headphones and the fact that you are hearing grain even at low volumes might seem to rule out the room as the primary culprit, my guess is that you are not going to get where you want to be without some attention to the room.  Personally, I've never listened to music in an average sized untreated room that could provide a satisfactory listening experience.   Low frequency smearing is commonly  recognized as room related, but anytime you have a failure of higher frequency signal to smoothly and rapidly decay, you will also get a smearing in those frequencies.  Not sure that necessarily comes across as grain, but it will come across as poor definition and articulation especially as the volume is increased.  I'd think about some work in this area after you've gotten your power supply and cabling optimized. 

What is your experience with solo violin recordings?  Are you good with how the Bach sonatas and partitas are presented?  How about the Beethoven sonatas?  Try some piano trios.  Are these works all presented without the grain you are objecting to?  How about sopranos and flutes?  What happens if you turn the volume up so that you are getting sound pressure levels in the high 80's and low 90's where high frequency instruments predominate?  If things other than grain go south when you turn the volume up, I tend to think about some room involvement in the problem, although equipment can't be ruled out. 

No easy answer here.  But I would go after clean power first.