How to set up and down limits on linear belt drive opener

If the closer has adjustable limits and are not set correctly, then it behaves normal. Time to set limit to correct door position.

Check your user guide if available. It sounds like you haven't set the door open limit, so press the up arrow & fully open to the door & push set, do the same for the down arrow until door is completely closed. Push the set button again & the door should be right..

how old are the batteries in the remotes. Hard wired remotes usually don't have a wire length limit.

Notes on replacing drive sprocket on Genie 2042 belt drive garage door opener.
The unit originally came with a cast metal sprocket disk with a plastic sleeve insert that formed the sprockets themselves. The plastic insert's sprockets shattered when I tried opening the garage door that had frozen shut with ice. Genie's service assistant was of no help, as she suggested that I remove the entire rail then call them back. Removal of the rail was totally unnecessary. I purchased an all metal sprocket designed for the 2042 from an on-line supplier. Neither the owner's manual nor on-line instructions were available to assist me. I followed these steps:

1.With the door open, loosen the tension on the belt by turning the bolt in the tension assembly located on the rail opposite side of the motor. Slide the belt off the pulley and let the belt hang.
2.The sprocket housing is located on top of the motor. Unscrew the two Phillips screws that hold the sprocket housing onto the motor assembly.
3.Using a screwdriver, force the cover up. The cover is on a hinge-like appendage that is riveted onto the rail frame. With the housing pried up, the belt and sprocket can be seen.
4.Pull the belt out of the housing to allow the old sprocket to be removed. Be careful to locate the black plastic bushing/spacer on top of the old sprocket and save it for the new sprocket.
5.Install the new sprocket and bushing/spacer into the motor shaft along with the belt.
6.Replace the two Phillips screws on the sprocket cover.
7.Place the belt back on the tension assembly and tighten to manufacturer's specifications.
8.If the motor won't run from the wall switch, the up/down limits need to be reset. The motor will move the garage door up and down using the control buttons on the bottom of the motor unit. Follow the manufacturer's instructions on setting the up/down limits, which include holding the "set" buttons for over 5 seconds once the garage door is in the desired up and down locations.

press the learn button on the motor, then you have 30 seconds to set the button you wish on the remote. make sure to do it within 30 seconds

You said you adjusted the up limit already. Is it adjusted as far as possible? Usually the screw will become harder to turn. You mention a new door and spring but is the opener the same? My guess is you have a new opener as well and it is out of sync with the trolley. Try turning the up limit back and see if the trolley will stop shorter. If it does, loosen the chain or belt so that you can remove if from the opener's drive gear. Bring the trolley to your stop limit and put the chain/belt back on the gear. Adjust the chain/gear tension and try door operation again. If it was a sync problem, the door should close closer to your limit. Adjust up and down travel as necessary to fine tune it. This worked for me so good luck.

BE SURE YOU HAVE THE CHAIN/BELT INSTALLED PROPERLY.
IF THE DRIVE IS AT OR NEAR THE UP LIMIT SWITCH THE DOOR CAN'T GO UP.
LOOSEN & REMOVE THE CHAIN/BELT.
TRY RUNNING THE OPENER TO BOTH LIMITS - JUST TO SEE IF IT WORKS.
RUN THE OPENER TO THE DOWN LIMIT.
MOVE THE TROLLEY TO THE CLOSED POSITION - RECONNECT CHAIN/BELT.
HOPE THIS HELPS

THE TRAVEL ADJUSTMENT IS ON THE SIDE.
YOU MAY BE ADJUSTING THE SENSITIVITY (TRAVEL LIMIT HAS NO MAX ADJ.)
BE SURE TO RESET THE SENSITIVITY ADJUSTMENT TO ABOUT 1/4

HOPE THIS HELPS

You need to adjust the limit settings. There are two white screws on the side of the opener. One adjusts the down limit and the other adjusts the up limit. One full turn adjusts the door approx two inches, so turn the screws in small increments and see how much more to adjust.

The close setting limit switch needs adjusted. Once it is adjusted it should work just fine.