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More clearance equals higher action so using lower frets isn't going to solve this problem, you'll simply be recreating it.
The problem is string stretch. It is the basic problem with all fretted instruments.
The solution is to compensate for it.
This can be accomplished through an array of solutions, NONE of which is perfect.
Compensating the bridge affects the fretting up the fretboard.
Compensating the nut affects down the fretboard.
The fretboard layout itself can be compensated. One such solution is a just intonated fretboard...you don't want to do that one.
Low action with a compensated bridge is the standard compromise. This works okay and usually has the middle range of the instrument playing acceptably.
If the action is high and everything else is properly laid out then correcting for sharping of the first few frets is accomplished by compensating the nut. This can be done by trimming a minute amount off the nut end of the fretboard but a more elegant solution for an existing instrument is to use a wider nut allowing it to overhang the fretboard and cut the compensation points into it.
Look up compensated nuts on classical guitars for information.
A downside of compensating the nut is that you're committed to the string gauge compensated for, any change in gauge will alter the effects of string stretch and negate the compensation.
If your guitar is tuned GDg or any G variant you'll have to pay particular attention to the compensating. The G string is usually the most noticeable string needing compensation.
Tuning also plays into intonation, equal tuning will leave some chords sounding a little off. Tuning is therefore usually adjusted slightly till it "sounds right" meaning that the sweet spot where most everything sounds good is found.
This varies with each players ear, don't think so, hand an instrument to someone that plays and chances are they'll adjust the tuning.
Jolly good tussle...On a fretless, if you draw the fret lines on the board incorrectly and play over them, certainly you will play out of pitch...LOL I know after the smoke clears, usually the solution will appear...Enjoy my friends.
I wouldn't break out a strobe tuner, but I would hope that when I "fret" (with a slide) across all strings at the 12th fret with enough pressure to get clean notes, that all of those notes will be close to true octaves of the open strings. Setting up the bridge so that will happen is called intonation. I played fretless bass for years and if you're jumping around the neck you rely on markers. So yes, the strings need to be intonated so that the "fretted" octave falls on the 12 fret marker.
To answer the OP, you can get intonation with high action. What you're describing (sharp lower frets) sounds like a high nut. I would set up the nut normally (so that when the string is held down between the 2nd and 3rd frets there is barely a gap between the 1st fret and the string) and raise the bridge to where you want it. Then, set the bridge back to compensate for the sharpening until the fretted note at the 12th matches the harmonic there.