ABitRusty said
That E string can be a booger.  Still fighting it myself but I think its getting better.  Pretty sure its a normal thing when learning violin to have E string issues. 

 I hate to jump into the change string category here but that may be something to try.  Not the whole set just different E's.  The tzigane E seemed ok and the obligato gold is what ive settled on for the moment.

It also sounds like youre experimenting with different attacks, pressure, and speed so thats good.  Possibly going sideways with bow maybe?   not saying just a thought for something to check.

also rosin buildup and maybe too much on bow.. Im constantly wrestling with that.

  

Currently I'm using the full Larsen Tzigane set.  It's ok but not what it's advertised to be, which is "warmer."  I might have to go to full gut strings to get the tone qualities I want, but not right now.  Not next year either.  Or maybe even the year after that.

Re: Rosin buildup...

I saw a video by one of the major string makers who recommended taking a soft dry toothbrush to the bow hairs on a weekly basis.  I've been doing that and I believe it's to help keep the rosin from building up (the video didn't say why other than "general maintenance") on the hair.  It certainly makes the brush sticky and I can see a line of excess rosin from the hair about halfway up the bristles so it's doing something.

I also clean my strings after each session with a microfiber cloth and clean weekly with alcohol on a tissue.

I'm trying to get that smooth/even tone on the E string that's in all of the recordings of the pieces and not getting there.  I can only assume that the players are a lot more experienced and that's the reason they sound like they do.  Of course this is rebutted by the fact that there are recital videos out there of 6 year olds playing the same way so I have to take the hit and admit that it's me and my playing where the problem lies.

I'm just wondering if higher quality bow hair is part of the difference and if it's time to trade up.

@SharonC

I've watched a ton of videos on "how to get rid of the E string screech" and they all discuss moving up the contact point toward the bridge the higher you go on the string.

I'll probably replace my current bow with something better eventually.  At this point I'm leaning more toward a wooden bow but the carbon weave bows get good reviews.  It won't be immediate, but I'll probably upgrade within a year.  We shall see I guess.

Gordon Shumway said
It's possible you are using too much bow speed and not enough bow pressure. It's also possible that just before playing the string a stray lefthand finger is accidentally touching the E string and setting up a harmonic or simply preventing the string from vibrating properly.

  

Anything is possible.  However, what if it isn't me?  Or partly me and partly the violin?

THAT is the question I have no answer for other than to say, based on several videos from self-professed luthiers on youboob, the measurements on my violin put my soundpost about 2mm further toward the centerline than the bass bar.

I won't mess with it.  Something like that is above my pay grade at this point in time.  Which means that for now I have to live with it until I can find a luthier who will return my messages.  There's a cello luthier in Santa Barbara I've hesitated to contact but her website does mention luthier services so... maybe.

At some point I will have to consider upgrading my bow.  A student bow will take me a long way, but eventually I will need something more capable of delivering better performance if I wish to continue to progress in my studies.  I have a long way to go before I get to that point, but I will eventually get there.  When I do I'd like to have enough knowledge to make a good choice.