I had a plumber friend review the building work and he recommended that it is done differently. While away on hols he came in and stripped out all the old plumbing for the radiator and the outside tap and replaced.
The outside tap is now in the car port, going straight out through the kitchen wall. The radiators run under the floor insulation, but now in 10mm plastic flexi pipes feeding off the 15mm main pipes. The pipes then run up the wall behind the radiator, so mostly out of sight.
New fittings and pipes in the wall
New pipe running across the floor. No crossover, all under the insulation in a channel cut through.
Pipes come out of wall behind the radiator so will not go through the screed floor at all.