An amp behind the TV is unlikely to help you much.

Long story short, an amp can't make the signal "better" at the amps output that is was at the amps input, but it can only beef the signal up to overcome down stream losses.(a good one can remove interference such as LTE). 

The purpose of amps is commonly miss-understood. Amps are not intended to restore a bad signal as you seem to be needing to do. If putting an amp right behind your TV fixed all problems, they'd simply build an amp into all TV's.

Splitters and long coax lengths reduce the signal strength (and Quality). An amp behind the TV can not restore information which has been lost up-stream of it. Once the data is gone, it is gone. By removing some of the extra/bad connections you have reduced up stream losses, retaining more of the signal/info, which is what has improved the picture.

The purpose of an amp is to preserve quality, not repair a bad signal. They boost the size of the signal at the antenna so that after the signal has been halved and halved again from running through all the splitters, cables and dodgy connections, the signal that arrives at the TV is hopefully the same strength and quality that left the antenna.

Amps also boost the noise, so in all professional installations amps are located at the antenna (or very near to it) because this is where the signal to noise ratio is at it's best. Down at the TV the signal to noise ratio will be at it's worst, so there's usually no point amplifying the signal there. In the TV diagnostics menus, signal to noise is most closely related to the Quality/BER figure and not the Strength. Quality/BER is the most important of the two readings.

Another point to keep in mind is that the antenna could be bad or miss aligned. Domestic antenna's are made cheaply and don't last forever. They commonly have very poor weather proofing and corrosion resistance, but people simply don't want to fork our the cash for decent antennas (made of stainless etc). If the design was particularly poor and the installation careless their failure is faster.

There's no mention of "BER" in the Sony Diagnostics screen.

I get what has been said about amplifiers. Although I'm hoping to increase a poor signal, compensating for losses in the splitters may well be enough as removing them shows a marked improvement. I guess trying out one of these gadgets from JC is the best bet. If no improvement I can return it. There's a great signal on Maori TV and a rotten one on 3. Is this my aerials fault, or are the transmissions at a different strength ?

IME the antenna's fail most frequently because they are subject to the harshest conditions but we have evidence that seems to point to your system needing a mast-head amp and that amp to be faulty (ie the power supply that makes no difference).

The channels are generally transmitted at the same strength but I'm not familiar with your area. Differences in reception are most commonly because the different frequencies bounce differently and the reflections can cause stronger and weaker final signal at the antenna/receiver location. Someone down the road could have exact opposite symptoms. When the signals are weak overall, some channels may be just above the threshold required for a good solid picture and some might be just below. Digital does a good job of making a flawless picture out of a weak signal, so your "great" channels might only just barely be good enough and not necessarily a good strong signal. Any component in the system (antenna, coax, splitter, connectors, bad mast head amp) can be the culprit in theory.

An amp behind the TV won't give the same results as the same amp at the antenna.

Thanks to all for feedback and advice. I'll ponder what to do next and probably get someone in. Will flag the amp idea.

It may be "good enough" now that the extreme pixelation seems to be gone. Will give it a few days.  I can't remove all splitters, as the first in line  is not accessible.

Thanks again, Cheers.

Poor on one and good on another is also a symptom of a bad join etc causing reflections in the cables, and also cross modulation from a crap amp being overloaded by LTE or other nearby stuff.

If the first splitter isnt accessible you have no way to know if its even terminated correctly so work on getting access to it, or running another cable around where it is located. Also give whoever made it inaccessible the bash if you know who they are.

Would it be worthwhile to change the mast head amp?  I can see there is one, a grey box about 3/4 down the hockey stick.
I have checked the Kingray power injector and it's just over 18v off load. But certainly it does not improve the signal when connected.  I assume it should ?