[paulp1960]

Just curious a lot of Tele and Tele type guitars cancel hum quite well but only on the middle switch setting with both pickups engaged. Does your guitar do that?

I wouldn't personally try to use a plugin effect to reduce hum after the recording. I would instead try to get the hum levels lower at the source.
Hopefully your new amp is not the hum source.

You might just have a very noisy environment

You could certainly replace the pickups with hum cancelling ones. The Dimarzio Area T pickups sound great to my ears, still like a Tele should sound but are very quiet.

It's good advice though to see what you can do with your guitar as it is now though, it is a fine guitar.

I like your tune I think you will enjoy the electric guitar.