what is your motherboard?
"1 long and 2 short beeps " with some manufacturers is a GPU error, others could mean bad memory.
beep codes are the motherboards warning bells, there should be a list to cross reference what the beeps mean.
it will be specific to your motherboard or motherboard manufacturer.
Motherboard is AMI, i did google those beeps and found the same Info you mentioned, but after swapping the Monitors back the beeping disappeared...what makes me think the GPU cant be really the problem here
are you positive the beeping is coming from the buzzer on the motherboard?
disconnect the speaker and try again. verify the trail so to speak.
the beeps and the GPU behavior are at odds.
download speccy its a program that will list the specs of your system and post your motherboard and GPU models as well as the power supply information. you may need to open the case to read the PSU label.
Canned Grounding Rant-
shut down system and remove side panel. with the power cable plugged into the PSU touch a bare unpainted metal area of the case. (my favorite spot is an unpainted screw securing the PSU) once you have grounded yourself you can unplug the computers power cable from the PSU and can touch the system.
if you move your feet, or shuffle in your chair, plug in the cord, reground yourself and unplug again.
end canned rant-
After Disconnecting my Dport-cable completely from the Monitor and using HDMI, the beeping is gone. So it seems like my GPU is getting some form of error while being connected with my Monitor via DP. I also remembered this started to happen only after i updated to the newest NVIDIA drivers ( so i am able to use the Freesync feature of my Monitor with my Nvidia GPU)
Motherboard: Z370-A PRO MSI
GPU: Nvidia Geforce 1070 Asus