Fibre cable
Best bet is to call your service provider and ask them for a cost to relocate, if that’s your key aim. Dropouts (could cover a multitude of things) are typically caused by factors on your own side of the network, such as WiFi. So best to ensure that’s not the case with further testing, by directly connecting using an Ethernet cable to the ONT where the fibre cable terminates. Again your service provider should be able to help.
Repairs (where it’s the service providers issue are free) but internal relocation of their equipment and cabling, they may charge a nominal fee which may be less than what you think.
Fibre cables aren’t as robust as copper and need care to ensure they’re not bent beyond a certain point otherwise they can fracture / fail internally and any connectors need to be similarly carefully handled etc. end faces in particular are susceptible to dust and finger prints if they’re not capped. Best to leave that to someone who knows what they’re doing / responsible if it all goes wrong.
Good luck.