I would not upgrade the contract, even if you go beyond your 50mbit UPLOAD speed you won't be sure that no buffering and hence drop in streaming will happen. Note you have a "500Mb Broadband" contract but the upload is limited to 50Mb. Asymmetric bandwidth is typical for "consumer" internet you mostly consume/download - contrary to "hosting" internet uplinks which typically are symmetric and very pricey since you are typically hosting/uploading.
You need specialised software to make sure you can transmit big, uncompressed real-time data (which video basically is) over the internet. It's basically what Youtube does for its users.
It hosts arbitrary uncompressed video data you upload to it (this is your NAS - which you have now) and then displays that data to users on the web in a compressed, streaming fashion (this is what streaming software would handle - which you do not have yet).