Dont think it can do any harm, mean you got another 2 degrees to go yet anyway lol

But will just cost more to keep it that hot

What about your hot water comming out the taps wouldve thought that was going to be the 80 degrees, which in reality is a bit hot (scolding risk if young kids in the house )

Dont know why the rest of the house wont heat, probs as you say you are trying to heat too much of each rad with missing doors. The rads should be specced to the size of the rooms they are to heat just not ones that look right lol. the temp of the water flowing round them should affect how quick they actually heat to the desired temp, but once that reached the rad stats should stop the flow of water round them to stop the temp getting unbearable.
The fact yours arent doing the job of heating even tho you got a temp of water flowing round them way in excess of what you would want suggests undersize rads compared to the area they gotta heat, which could be down to the missing bits.

One thing just crossed my mind espescially if the water comming out your taps isnt rediculously hot, is what is the digital stat reading celcious or faranheight ??? 80 degrees farenheight is only 26.5 degrees centigrade

Steve