funny - i only notice the urine smell in the summer - when it's really hot. i don't have a/c, but i do have big trees. i always open windows at night and close up the house during the day. when we have those weeks of hot days and hot nights, my house gets really hot and humid. that is when i notice the urine smell. maybe taking off the cover and spraying the fins/pipe with a clorox/water solution until it drips down on the floor and you just wipe up the floor. i don't know how else you can clean those things.

i'd cost out a new heater unit. in the end it might not be nearly as much as you think, the wiring is all good to go.

There's nothing really mechanical in your baseboard if it's a hot water baseboard. It shouldn't hurt hurt to spray it. Instead of bleach, consider using a pet urine neutralizer. Urine has ammonia and you need to neutralize the smell.

I noticed the rust on the baseboard cover. Rust is an absorbable surface so it will trap odors. A quick sanding and some paint will fix that.