It seems I have been summoned....
Unfortunately it's difficult to explain the ins and outs of violin writing in any reasonable span of text, especially virtuoso writing. The more difficult you want to make your part, the more nuanced of an understanding of the instrument you must have, and this comes with actual hands-on experience playing the instrument at that level.
Of course that isn't to say you can't still write virtuoso music. Saint-Saens was hardly a violinist, after all, but many such non-violinist composers seeking to write difficult violin music did seek the advice and feedback of violinists in their compositional process, often sending them drafts and allowing them to make edits. They employed what is most likely the best approach to such things: write whatever you want, and worry about whether it's playable later. Violins are probably more agile than you may think they are.
I'd heavily advise against just trying to create virtuoso writing purely for its own sake. That is a surefire way to heavily compromise the musical integrity of what you're writing and it can really destroy any musical inspiration you may have.
Concentrate on writing a nice tune first, then try to develop it with flowery embellishments calling for virtuoso technique. Not only will the fundamental idea underlying the piece be clearer to the audience, since its first appearance will be clean and unornamented, but I honestly even think the virtuoso writing will come easier after that.
Interestingly, something I wrote a while back comes surprisingly close to fitting the profile of what you seem to want to write: my Romance in D (2020). It's monothematic (i.e. there is no "B theme" to speak of) and a little longer than your target, but it is still steeped in romantic-era conventions and is basically in ternary form with a coda (the middle section is bookended by the double bars). The accompaniment is fairly simple throughout (mostly block chords and arpeggios); you don't need to spend a lot of time fretting about making something super novel or complicated. The only real secret is an attempt to adhere to good voice leading, particularly with the bassline, though you may also hear some somewhat melodic-sounding lines in the right hand as well, which makes it sound interesting, even if it's very simplistic at a fundamental level. (This is why we study Baroque counterpoint -- its principles are universally applicable to all common-practice tonal music.)
You'll notice I used many of the strategies I promote here, such as presenting a relatively unadorned melody at first before embellishing it the next time around. Like I was saying, the exact strategies for achieving good virtuoso violin writing are hard to put into a small number of words, but obviously everything I wrote here in this piece is playable (since both me and my accompanist played it), so similar-looking techniques in your piece should also be playable.
I took a listen to your previous work, and it seems you already have the ability to write a good melody based on a motivic cell, so I won't go into that much, but I do want to reiterate that it is a very powerful compositional technique that I also use in my Romance. (My main motivic cell is a rising triad in quarter notes.) It lends the piece a great sense of unity and forms powerful recall associations in the listener's mind that keep them believing that whatever material you're showing them now really does belong in the same piece with what they heard before.
Just be careful to avoid writing anything that is impossible on an elementary level, such as double-stops in which both notes can only be played on the G-string. Otherwise, focus on compositional integrity, substance, and sound first. The explicit aims for virtuosity come later.