Your "how it should look" looks pretty good to me as is. But I think that your issue is trying to beam through the 16th rest at the end of bar 1. Don't do that. It's at the very least confusing; beaming two notes together is one thing and rests are another, so the group you have there creates a reading conflict that has to be sorted.
So, I would say just make your last note (FC) with an upward stem and a flag, exactly as it is at the beginning of bar 2. Then you can tie them.
Ditto for the last 16th note in each bar with the tiny stem. Don't beam it with the previous note. Do it the way Old Brixtonian has it in his answer.
Finally, there isn't any such thing as notes in the bass clef that are "technically in the treble clef." That's like saying that something purple could "technically" be yellow. Seriously, though I think what you are getting at is notes above middle C that are written in the bass clef. That is done all the time; it's whatever works best.
For some ideas from a master composer, have a look at all the tricks that Liszt pulls in his Un Sospiro to make his intentions clear. Look also at how the performer breaks up the melody and arpeggios between the hands. You will probably find it instructive to study this piece in some detail:
In the first measures before the melody comes in, it's typical to take the notes in the bass clef in the left hand and the treble notes in the right. Once the melody comes in (written in a second treble clef for clarity, the usual fingering is to alternate the left and right hands (see if you can work out why), as you see the performer doing here. That is the basic way to finger most of the piece, even as Liszt begins to add extra notes in the melody as he is so fond of doing.