There is a lot of info there - thanks to both.
For broadcast TV the television decodes the broadcast signal natively, meaning the TV can handle the internal processor handles scaling and de-interlacing without an intermediary device altering the feed.
That makes sense - maybe part of the effect is caused by the EE box only using 60Hz I seem to remember? The idea of "native" decoding by one device is probably on point as I have proved this many times with audio feeds where as soon as you insert extra signal handling or processing in the feed, to tailor frequency response (DSP) or gain etc., it will lift/cut the bass, treble or whatever you have selected BUT the resultant audio never seems to quite "gel" or be complete?
Once the TV confirms the LNB still works, if two tuners is enough, possibly seek out an old Humax Foxsat-HDR and install the custom firmware / patch on it...

You may seldom need to record more than two channels and could use the EE box for those occasions; or even the TV with an attached usb hard drive.
Funnily enough I had a Foxsat HDR originally, complete with CF and the patch, and it worked very well apart from the occasional pixelation breakup on the picture which I discovered was caused by my router WiFi which was only about 3ft away from the dish! That problem was resolved but I ended up not using the Foxsat very much because the UI was so painfully slow. The HDR T2 was much quicker so that became my main machine and it was very easy to transfer items for long time storage onto my NAS. I sold the Foxsat a while back before all the concerted efforts to convert every man and his dog to Freely, no recording and the "You Will Watch Adverts" or pay extra conspiracy!
Picture quality / appearance may well be due to per input settings differences... so internal tuner uses one set, internal streamer another, and the hdmi input from the EE box a third... Tweaking / copying settings is usually simple enough.
Note that the EE box may also do a worse job of upscaling cf the TV so try that as well.
Your eyeballs are what matters. So set things to suit you!
I have tweaked the per input setting suitably although it was a lot more logical on my previous Sony set! As for SD upscaling - I avoid SD like the plague and will only ever use it for something that I absolutely must watch that cannot be found on HD - very rare!
I remember when I had both types of Humax at the same time I had to tweak the picture settings on each input to the Sony TV quite differently to get a similar result.
As for HDR content, the first few times I experienced it on the LG TV I thought it was horrible - like the saturation had been cranked up to 100% along with extreme contrast and colours! That was very soon resolved and now gives very pleasing results. That is one thing the EE box fails with - if you have been watching HDR from it then when you exit the feed, from Prime for example, it still stays locked to HDR output whilst you navigate around the home page or guide etc and only "drops" the HDR output to the TV when you actually select a different feed with the result that the menus and guide are rather "glaring"!
I must say that some of this technology is getting extremely complicated and the user is expected to be cognisant with so many technicalities and so much terminology which I am sure leaves Mr.Average shopper completely confused, resulting in most things staying at oob default? It would be good if the TV used AI to ask "Is you picture satisfactory?" to which you could reply "a bit too red, bright, dark, low contrast, bla, bla....." and it would tweak the relative settings for you - per input and type of signal of course!