Since "knuckle" can get a little confusing (you have three on each finger), I'm going to use the "official" definitions of the parts of the finger, as given by http://www.simplybodylanguage......names.html.

• Tip segment: Distal phalanx.
• Middle segment: Middle phalanx.
• Bottom segment: Proximal phalanx

If you're talking about your proximal phalanx, or the knuckle between it and your palm touching the side near the E string, I understand the problem. I have it, too, although I don't really have a vibrato yet, so it hasn't been an issue for me.

I don't think you need to bring your hand over more (which is what bring your elbow further to the right would get you), you need to bring it UP more, and twist the hand more to get the finger back down where it needs to be. For me, that does put more stress on the shoulder and triceps, especially when the hand is extended far out. Twisting the hand more puts more stress on the forearm.

Since it's related to how far out the hand is, there are two possible answers. Practice it (gently) until your body adapts, or get a smaller instrument.  I'm guessing the problem is worse on the viola than the violin?

I just tried an experiment, related to some stuff my teacher has been wanting me to try. Since you don't use a chinrest or shoulder rest, this may work well for you.

Put your chin on the RIGHT side of the tailpiece. This will make it just as secure as on the left as far as pulling away from your neck, and more secure about slipping forward. It will allow you (force you, really) to move the neck considerably back, which is a much more comfortable place for your left hand.  I find it somewhat less comfortable for bowing, but not impossible.

The biggest downside is that I can't really see what I'm doing.  For the left hand, that's not a problem - I can tell by ear whether I'm getting it right or wrong. For bowing, not so wonderful.  A mirror would probably be a necessity until you learned to tell by feel whether your bowing is right or not.  For an experiment, it can be lived with.

Play a few easy things to get halfway adjusted to it, then try some of the vibrato stuff, see if it makes a significant difference.  It's a MUCH better angle for the left hand, so I'm suspecting it will.

According to my teacher, this is the way violin was played before chinrests and shoulder rests came along. They also played in sort of a 2nd position, reaching way up to play what we consider 1st position. The heel of the hand was used to tilt the violin back and forth to make hitting the various strings easier.  I have no idea whether I'm going to go to that style, but I'm going to experiment with it some, because I haven't found a chinrest yet that works for me.

Same for you - I'm not suggesting you should switch to this style, but I am suggesting you should work with it for a while and see if it, or any pieces of it, work for you.