Heating systems aren't ever balanced. I've been round a few with a surface thermometer, and never found one close to being balanced. I tried to balance my own like that, and gave up. As long as they have enough flow for all rads to to heat up, let the TRV deal with it.
If you have one rad, say a towel rail, near the pump wide open, the system won't work, but I've not met anyone using more than experience and educated guesswork to get it going.
I balanced my mother's radiators by reading the temperature reported by the TRV, if the current exceeded the target, which as first set up they all did, then I closed the lock shield a tad. And all but living room, the rooms were then spot on the setting. Living room it was sun through the bay window causing the problem, not the central heating.
I've put a few plinth heaters in, like the Myson ones with a fan which comes on when the pipe gets warm. They belt heat out even on lowest fan setting. Those use a cross flow fan which can be silent
The Myson has a completely different method of control, better in series not parallel as you do not throttle them back with a lock-shield valve, I had the output go into a standard radiator in the same room, so it did have a lock-shield valve, but having two radiators in series caused enough resistance to flow, to prevent it starving other radiators.
I put the fan in to primarily make the TRV see the actual temperature.
This was basic to the idea in the room where I tried to use a fan. It was a long radiator, and fan opposite end to the TRV, and I used the thermostat I had for the brewing to turn on the fan, the sensor at the TRV end which was the return. I opened the lock shield a bit more than it should have been, but the sequence of events were, heating turned on, return pipe got to over 25ºC, fan started, return temperature dropped, fan stopped, and the cycle would repeat.
Tried opening the lock shield more until fully open, and still this on/off sequence. Next was a smaller fan, the only one which worked with any sort of success, was a small USB fan, which was so small hardly worth having.
One problem is the speed of the TRV, they exercise on Saturday midday, and to fully open then fully close, then return to setting, it would take around 3.5 minutes, and this does not include the time for the heat to reach sensors. So on boiler turn on the radiator could over heat unless the lock-shield set spot on.
So heating turned on at 7 am, ready for carers to arrive a 8 am, but set the TRV to 20ºC and at 8 am still only showing 19ºC if lucky, so would set TRV to 22ºC until 8 am, then go back down to 20ºC, seems the built in anti-hysteresis was OTT, by 9 am all radiators just warm, so if the sun came through the bay window it did not have to cool much to be cold.
Once I had realised I had to set the sequance on the TRV this way to defeat the OTT anti-hysteresis I found I did not need the fan, so that was abandoned, the biggest problem was the hall, there was no TRV on the hall radiator, and attempts to set the lock-shield to match the wall thermostat failed. Fitting a TRV to the hall radiator transformed the control.
It took some tweaking, the aim was, after the front door had been opened, and mother taken in or out in her wheel chair, we wanted a rapid recovery of the hall temperture, but before the wall thermostat turned off, wanted the TRV to have nearly fully closed so only on warm days would the wall thermostat turn off, so that the boiler modulated fully before the hall got warm enough for the wall thermostat to turn it off.
It work spot on, however tried to repeat the setting here with a non modulating oil boiler and it was a failure, the old Energenie TRV heads the batteries lasted well, but found the Kasa head in comparision eats the batteries, the eQ-3 heads are claimed to fail open, and since bluetooth one needs to be close to check battery is OK, so a few discharged batteries can mess everything up, with radiators heating up that should no.
Found with this house, cold room is because the central heating not running, TRV living room at the moment shows 22ºC, wife's bedroom TRV however shows 17.5ºC, the living room wall thermostat shows 23.3ºC and the hall wall thermostat shows 21.5ºC so neither of the wall-thermostats are likely to start up boiler to get wife's bedroom warm. Not that it is needed today, but the only way to get that boiler to run when she needs heat, is for the TRV heat to be linked, which it is that room has a Wiser TRV head.
But since her room and the office are likely the coldest rooms in the house, it is important that when only her room needs to heat, the other TRV heads in the house are closed. Can't stop pipes warming wall and floor, but can ensure radiators don't turn on unless, required, so office and dinning room not being used at the moment so TRV heads set to 12ºC, my bedroom turns down at around 9 am and does not turn up again until 10 pm, and living room turns down at midnight until 7 am, every room has its own schedule, and in the main this works well, meaning more central heating water available for the rooms which are in use. And for the rooms with Wi-Fi linked TRV heads (5 rooms bluetooth only) a simple command hey google turn living room to 22ºC does the job. Although 5 TRV heads are linked to Wi-Fi, only 1 is linked to boiler.
I do not regret getting the 5 eQ-3 bluetooth heads, at £15 each in 2019 that was good valve, but I think these maybe reused in the flat under the main house, but can't make my mind up on if Wiser or Kasa to replace them, there are also disadvantaged with linked to boiler, but looking at battery life before I decide.