Hello!

This has some potential as a galant-revival keyboard concerto.
When I read that you thought the harpsichord part might be impossible to play, I wondered to myself, "well, if you realise the part might be impossible to play, why would you want to write it that way?" When in doubt, be conservative.
As it happens, the harpsichord
concertato part is not the problem here at all. It's actually quite playable. What I'm hearing as a problem, to begin with, is the muddy interplay between the independent cello and contrabass lines. In this idiom, that's a big mistake...especially with so much going on down there.
I don't know whether you've ever examined the score of a baroque, galant or classical composition, but the cello and bass virtually
always double each other (an octave apart), and in fact are often written together on the same staff, with "violoncello e contrabasso" or "basso continuo" in the margin. The reason for that is that those guys discovered early on that when the cello and bass parts are separate and too independent, the result is a muddy mess in the bass register. The harpsichord part has the same problem, by the way...too much independent stuff going on in the deep bass. It all gets lost and turns to mud.
This problem is making your piece sound needlessly amateurish, but it is fairly easily remedied. I would very strongly suggest that you figure out a way to combine your 'cello and contrabass parts and have them play all the same notes throughout the piece (written the same, but sounding an octave apart). If you insist upon independent lines, then you simply must simplify the contrabass part and give the more active line to the 'cello. If you do insist upon it, understand that this would virtually never have been done in an 18th Century concerto - and you're clearly writing in that idiom. There are ways to make it work, but you'll have to be very careful.
The triplets in the viola don't work well overlapping the 2nd violin's straight quavers in exactly the same register. Stuff like that jumbles and gets lost.
In measure 3, there are parallel 5ths between the 1st violin and cello/bass passing from beat 3 to beat 4 (E to D in 1st Violin, A to G in cello/bass) - big "no-no" in this idiom, and it ends up sounding amateurish. Again, it's easily fixed, but it means a different choice of voicing.
I'd caution you to be mindful of what chords you're ending up with in your moving parts. Just because a part moves in what seems a logical direction doesn't mean it will sound good in the chord you end up with. It's disappointing to find that something you thought would sound good doesn't work, but it's worth the effort to find something that does work, even if it means biting the bullet and changing something we'd rather not.
A picture is worth a thousand words. I've attached just the opening ritornello with suggestions on just one of many ways it might be amended, based on your original melodic idea. What it lacks in "originality" it makes up for in functionality, and being closer to the established conventions of this idiom. And it "works."
I've also written in a "continuo" part for the harpsichord during the ritornello, just as a demonstration. Keyboard soloists in the 18th Century did not just sit and wait for the orchestra to stop playing the introduction before they launched into the
concertato part as they now do; they would play the continuo part to fill in the harmony. Even Mozart played continuo in his own concerti from the fortepiano (rather than the harpsichord), which was becoming more and more common in his day. By Beethoven's time, that practice was becoming a bit old-fashioned, but Beethoven was trained thoroughly in the art of continuo playing all the same, and he probably played at least some continuo in the orchestral sections of his concerti.
Of course, the continuo part would not have been written out...I have only done it to show how the player might have interpreted it. Note the figured bass I have written below the contrabass part - these figures would have told the player what chords to play in the right hand, or the player might have improvised something logical, such as what I put in the right hand of the harpsichord on beat 3 of measure 2 - that little run in parallel thirds isn't in the figures, but it follows what the violins are doing.
* sigh * - I've overdone it again. Oh well. I'm only trying to help. Best of luck to you on this!