Given the chaotic (but sadly not uncommon) state of the floor void: pipework, electrics, and general debris typical of any house built without care or modified on several occasions during its life, it doesn't surprise me particularly to hear clicks and noises. I do wonder whether the noise may have come into play when the boiler or pump was replaced and whether some of the existing pipes may have been moved or twisted very slightly and whether this may have led to them grip/slipping against adjacent surfaces during expansion or contraction phases while, perhaps, the air noise was masking these quieter sounds. Indeed it is incredibly hard to work on pipework that is not fully supported without moving it al least a little. That said, I may be going up a dead end in that I find it hard to entertain the idea that the F1 was a cause of the noise, and I may be wrong.
I do have a hunch (no more than that), that someone has fiddled with the balancing of the system. The balancing may now be out or it may have been out previously and is now correct (but is now making a noise it didn't used to due to the return pipes being warmer or cooler than they were in the past).
As every different company / plumber or any place will be like, everyone tells you different things. They said the speed of the pump should never have been touched and left on what it was when it got installed. They put it back to speed 3 which I still think is seriously overkill for a house this size with 7 radiators. The noise this pump makes is just too much on this speed. You can hear the hissing from it at ever radiator in the house. Basically making it sound like the boiler is in every room. I will try and get hold of them regarding the other sounds still being there, but despite what they say, I still plan to switch it back to speed 1, as the heating was just as effective at keeping the house warm with it set to this over the last year.
Essentially, the test for correct pump speed on a modern boiler is that, once the system is warm through and with all radiator manual on/off valves or TRVs fully open, the water leaves the radiators at a temperature no more than 20°C cooler than it went into the same radiator. This would be measured at each radiator; the flow though each radiator can be adjusted (called 'balancing the system') but the pump speed would be set to be fast enough for the radiator that seems to be least easy to supply sufficient water to.
In the old days, the old boilers were coupled to system that would give return water 20°F or 11°C cooler than the flow when the boiler flow was at maximum (around 82°C), but that was largely arbitrary and much to do with the need to avoid thermal stresses to the boilers of the day. This is relevant to you as your system would largely have been designed to work under these conditions: older radiators may not give enough heat on a 20°C drop, so your drop may need to be set at less than this.
At a guess, I would imagine speed 1 would be sufficient for 7 radiators, especially radiators of that age which are unlikely to require a huge amount of flow.
I can only guess that something really odd happened relating to the method they filled up the system when they added the F1 protector.
Or some small change that took place at the same time and they didn't even think to mention (I'm clutching at straws here!).
The picture of the audio is an hour of the heating in the evening. You can see just after 45 minutes, it switches off which gets rid of the pump noise, but then the clicks and bangs go crazy for a while. This was not the case until after the power flush, but may be related to the excessive pump speed. The audio attachment is the stage where the pump switches off. Where this is recorded is on the other side of the house to the pump.
Ticking noise certainly sounds like thermal expansion to me, and the plethora of ticking after the pump switches off would suggest thermal contraction.
I've also just found a video from ages ago before the system got bled and the F1 protector got added. This was well after we got our new boiler and pump. The heating instead sounded like the video shows unless all the TRVs were on full. Whenever they were reduced, it made this main radiator sound like a cold tap was running. This sound could be heard in my bedroom. This infact would still be far better than what is now the case with intermittent bangs. Something strange caused this, but I don't know what.
That running tap noise in the old video with partially open valves is the result of the water, pressured by the pump, squeezing through the restriction created by a partially open valve. It would be undesirable in a properly designed system, but can be unavoidable if modifications to an elderly system (such as fitting higher output radiators) means that the only way to shove sufficient water through some parts of the system without creating excessive flow in other parts is to up the pump speed. In such a case, the pump may need to run at top speed with some of the circuits heavily throttled back. Ideally, the radiator with the most restrictive (longest, usually) pipe run would have its valves fully open and the pump would be set just right to feed that circuit, with the rest of the radiators throttled down and you'd hope the pump would not then need to run so hard as to create this kind of noise.
From your description, I would suggest that what is happening is that the pump is set to a fixed speed (as all old pumps did - modern pumps can (if set to a proprtional pressure setting) vary their speed to give more flow when required and less flow when not required, but this setting tends to provide less pressure than the fixed-speed setting, so does not always work on a legacy system that might simply require more pressure). The fixed speed means the pressure increases when there is little flow through the other radiators, so, having nowhere else to go, it's getting shoved through your only non-TRVd radiator.
Sorry for all this info, but just trying to list everything I've tried to make it as clear as possible. I myself am desperate to reduce this noise as it is incredible disruptive.
I get it. Noise is, actually, one of the (several) reasons I switch my heating off altogether at night. Sometimes theory and practice don't quite go together and there are factors we cannot see. Which can sometimes be more annoying than the symptoms themselves!