Get foam weatherstripping for the door and a floor sweep for the bottom of the door.
You could even use one of those fabric tubes filled with whatever to block the gap at the floor.
Maybe hang a carpet on the door? Is the door solid core, hollow core or panels?
The LSX II LT are $999 on the KEF website.
They’re great for a small space.
Take a look at KEF LSX II, too.
They support a higher sampling rate when using the interspeaker RJ45 cable.
Since both models are fully powered there’s no need to buy an amp/integrated amp.
You can stream directly to them via wi-fi from your phone or computer.
I have the original LSX in my bedroom (about the same size as your room).
I added a KEF KUBE 10 subwoofer.
They’re connected to an Apple TV 4K, and a computer monitor for video streaming.
