We established long ago that your system has poor circulation, and replacing the pump with one that works will make a big difference. Stop fannying about and get on with it.
Once you've got the new pump, the water will be circulating better. If you can afford an extra £100 or so, get a Magnaclean fitted at the same time. This has a magnet that traps circulating particles of black iron oxide sludge (there is usually a lot of this in an old open-vented system)
After the pump is fitted and you are satisfied there are no leaks and it is filling properly, add a litre of Sentinel X400 (which is a very mild sediment-loosening chemical) and let the pump run through the radiators for 4 weeks (even if the weather is hot and you need to turn the boiler stat off or down)
You will know it is starting to work when the circulating water goes jet black (you will see it collecting in the Magnaclean if you have fitted one)
After 4 weeks, drain it out and rinse it to remove the loosened sediment. Add a litre of Sentinel X100 on final fill to prevent future corrosion. If you fitted a Magnaclean you will see it continues to collect more black sediment for a year or more, even though you thought you had drained it all out.
If the boiler still makes kettling noises, it may be limescale. Add a litre or two of Sentinel X200 and leave it in (do not drain). If you close off some of the radiators first, it will be more concentrated when you are running HW only, so will work faster.
The chemicals will cost you about £15 each from most DIY sheds or plumbers merchants. Avoid cheap brands. Also avoid aggressive chemicals or acids, they have their place but need a lot more care and can't be left in for long.
You know you have to scoop out the mud from the F&E tank, and sponge it clean, before draining? And you know that before adding chemicals, you tie up the ball float in the F&E and drain a couple of buckets out of the drain cock? So that when you untie the float after stirring in the chemical, it will be drawn down into the system.
I am a householder not a pro.
X800 is said to be faster than X400 but I have not used it.
During the warm weather, after draining out the X400, would be a good time to fit new rad valves and TRVs and new bleed nipples where needed. It saves draining down again later. You can do this yourself.