Reinstallation of radiators after insulating radiator niches

I have the following problem:
I have three radiator niches with thermal bridges. We have a gas central heating system in the house. I would like to have the niches insulated. The distance from the interior walls (niches) to the heating pipes is 4 cm in two rooms, and 3.5 cm in one room. The radiators are attached to the back walls with rails and brackets. Depth of the rails approx. 1 cm, depth of the brackets approx. 3 cm. I am quoting here the statements of two professionals:
With insulation boards of 5 cm thickness, there is the possibility to make a branch to the heating pipes. Then, in my unit and in other units in the house, water must be drained from the radiators in the heating system.
With insulation boards of 2 cm thickness, there is no possibility to reattach the radiators at the back (because of the aforementioned rails and brackets). There is also no other alternative to reattach the radiators at the back.
Option 1 is practically not feasible for me, as then several parties in the house would need to be involved. I do not need to comment on option 2.
I ask the professionals in this forum to comment on the issue, especially regarding statement 2.

Yes, option No. 1 or leave everything as it is.
Without draining the heating system, it won't work at all.

Hello. Well, there is one possibility, but beforehand I don’t know your premises. The possibility would be to freeze the pipes; there is a special device for that. Tip on the side: There are certain films to stick on that look like aluminum foil. The task of this foil is to reflect the heat that radiates backwards back into the room. Best regards ;)

Frozen yes if the pipelines are at least 10 - 15 cm long. However, it should be carried out by a professional.

Well, there is one possibility but first of all, I do not know your premises

As I said, best regards ;)

Hello Volker

There are vacuum insulations today that have very high thermal insulation and are thin. The price is indeed high, but you don't have to move the 3 radiators further away from the wall, which would involve welding work.

Freezing is a common method today for individual repair jobs - but it must be done by a professional. If applied incorrectly, the damage is greater than the benefit. ;)

Greetings from the coal shoveler