I'm not exactly clear about some of your question, so let me just describe the correct way to do it, and hope that answers your issue.
ANY breaking putt can be sunk by SOME combination of line and pace. More pace, lower line; less pace, higher line.
But pace is "smart" and steady and not really up for grabs according to what YOU might desire. A "smart" pace is simply 1) never short, 2) slow across a hole effectively wide, and 3) stops in a short space behind the hole so the next putt is easy for you, which is generally a ball that stops within 2-3 rolls or 2 feet behind the hole.
The INTENTIONALITY that your putt will stop like this is critical to the force your body uses for the tempo and rhythm of your usual stroke action. So ALWAYS INTEND TO STOP THE BALL behind the hole less than 2 feet. So the pace is simply "smart" and never changes.
That means that the LINE has to "come to the pace." YOUR smart pace must be KNOWN and FAMILIAR to you and not subject to change from one putt to the next. So I teach "rhythm first, read second."
This mean that your rhythm, set by your intentionality, always rolls the ball at the same pace past the hole to stop within 2 feet behind the hole. Make many strokes from 5-8 feet to stop past the hole like this using your REGULAR tempo and rhythm. Watch these putts and LIKE the pace as it goes past the hole. Only then can you "read" putts with your smart pace and adjust the line to your steady pace.
After missing many putts with perfect rhythm from 5-8 feet away, try seeing the exact last 1-2" of entry path center cut over the lip and then aim the start line and make the same rhythm and see what happens.
In your case, you don't have a stable rhythm and think that adjusting the delivery pace is okay and then have trouble with the line. It's not. Pace same, Line adjusts to pace.
The INSTINCTIVE WAY to read any putt is to imagine aiming straight at the center of the cup and predicting how that LINE will go lowside immediately, and then adjusting the LINE a little higher and re-predicting how far down the baseline that steady pace will now advance the ball before it falls to the lowside, and then aim a little higher LINE and re-predicting how much closer to the hole that same pace now goes before falling low, then adjust the LINE a little higher until the same pace sends the ball all the way as far as the hole before the ball falls to the loused. THAT LINE is perfect for the usual pace.
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