For being able to level the gantry with non metal plates on your aluminiumbed you need an alternative to the inductive probe.
The inductive (even the Fotek) had not enough range to go through my 3mm Ikea LOTS mirror. The nozzle allways punished the pei on that mirror.

You need to remove the original mount of the bl to make it fit the 2.1 carriage, see the pictures. For me it had an offset of 1.8mm.

Here my configuration example:

#####################################################

[probe]
pin: z:ar18
x_offset: 0.0
y_offset: 15.0
z_offset: 1.825
speed: 5
activate_gcode:
    SET_SERVO SERVO=bltouch ANGLE=10
    SET_SERVO SERVO=bltouch ANGLE=60
    G4 P200
deactivate_gcode:
    SET_SERVO SERVO=bltouch ANGLE=90
    G4 P200

[servo bltouch]
pin: z:ar11
maximum_servo_angle: 180
minimum_pulse_width: 0.0006
maximum_pulse_width: 0.0024

#######################################################

Theese is the repeatability on TMC2208 with klipper running at 16 microsteps with interpolation and 5mm probespeed in a 300^3 build.
I tried to produce a temperatur drift with enclosure to 60° and at 20° the mesures were the same in both cases.

#######################################################

10:39:12 probe at 60.000,40.000 is z=1.780000
probe at 60.000,40.000 is z=1.802500
probe at 60.000,40.000 is z=1.805000
probe at 60.000,240.000 is z=1.805000
probe at 60.000,240.000 is z=1.807500
probe at 60.000,240.000 is z=1.807500
probe at 240.000,240.000 is z=1.807500
probe at 240.000,240.000 is z=1.805000
probe at 240.000,240.000 is z=1.807500
probe at 240.000,40.000 is z=1.805000
probe at 240.000,40.000 is z=1.807500
probe at 240.000,40.000 is z=1.802500
Making the following gantry adjustments:
stepper_z = 0.021571
stepper_z1 = -0.011392
stepper_z2 = -0.000952
stepper_z3 = -0.009227
10:41:27 probe at 60.000,40.000 is z=1.795000
probe at 60.000,40.000 is z=1.812500
probe at 60.000,40.000 is z=1.820000
probe at 60.000,240.000 is z=1.800000
probe at 60.000,240.000 is z=1.807500
probe at 60.000,240.000 is z=1.802500
probe at 240.000,240.000 is z=1.802500
probe at 240.000,240.000 is z=1.802500
probe at 240.000,240.000 is z=1.802500
probe at 240.000,40.000 is z=1.805000
probe at 240.000,40.000 is z=1.805000
probe at 240.000,40.000 is z=1.805000
Making the following gantry adjustments:
stepper_z = -0.010663
stepper_z1 = 0.005064
stepper_z2 = 0.003166
stepper_z3 = 0.002434
probe at 60.000,40.000 is z=1.812500
probe at 60.000,40.000 is z=1.815000
probe at 60.000,40.000 is z=1.815000
probe at 60.000,240.000 is z=1.802500
probe at 60.000,240.000 is z=1.807500
probe at 60.000,240.000 is z=1.802500
probe at 240.000,240.000 is z=1.805000
probe at 240.000,240.000 is z=1.807500
probe at 240.000,240.000 is z=1.807500
probe at 240.000,40.000 is z=1.800000
probe at 240.000,40.000 is z=1.802500
probe at 240.000,40.000 is z=1.805000
Making the following gantry adjustments:
stepper_z = -0.023831
stepper_z1 = 0.013795
stepper_z2 = -0.008034
stepper_z3 = 0.018071
10:54:42 pressure_advance: 0.050000
pressure_advance_lookahead_time: 0.000000
11:08:29 pressure_advance: 0.100000
pressure_advance_lookahead_time: 0.000000
11:43:17 Klipper state: Disconnect
11:43:22 Klipper state: Ready
11:44:12 Klipper state: Disconnect
11:44:17 Klipper state: Ready
11:44:37 Unknown command:"FIRMARE_RESTART"
11:44:52 Klipper state: Disconnect
11:45:02 Klipper state: Ready
11:45:07 Klipper state: Disconnect
11:45:12 Klipper state: Ready
11:47:44 probe at 60.000,40.000 is z=1.342500
probe at 60.000,40.000 is z=1.367500
probe at 60.000,40.000 is z=1.370000
probe at 60.000,240.000 is z=1.925000
probe at 60.000,240.000 is z=1.925000
probe at 60.000,240.000 is z=1.922500
probe at 240.000,240.000 is z=2.110000
probe at 240.000,240.000 is z=2.107500
probe at 240.000,240.000 is z=2.112500
probe at 240.000,40.000 is z=1.875000
probe at 240.000,40.000 is z=1.882500
probe at 240.000,40.000 is z=1.882500
Making the following gantry adjustments:
stepper_z = 1.165117
stepper_z1 = -0.370766
stepper_z2 = -0.413474
stepper_z3 = -0.380877
11:49:56 probe at 60.000,40.000 is z=1.842500
probe at 60.000,40.000 is z=1.862500
probe at 60.000,40.000 is z=1.865000
probe at 60.000,240.000 is z=1.847500
probe at 60.000,240.000 is z=1.847500
probe at 60.000,240.000 is z=1.845000
probe at 240.000,240.000 is z=1.830000
probe at 240.000,240.000 is z=1.832500
probe at 240.000,240.000 is z=1.827500
probe at 240.000,40.000 is z=1.835000
probe at 240.000,40.000 is z=1.840000
probe at 240.000,40.000 is z=1.845000
Making the following gantry adjustments:
stepper_z = -0.028856
stepper_z1 = -0.009106
stepper_z2 = 0.028856
stepper_z3 = 0.009106
probe at 60.000,40.000 is z=1.847500
probe at 60.000,40.000 is z=1.847500
probe at 60.000,40.000 is z=1.850000
probe at 60.000,240.000 is z=1.835000
probe at 60.000,240.000 is z=1.837500
probe at 60.000,240.000 is z=1.840000
probe at 240.000,240.000 is z=1.835000
probe at 240.000,240.000 is z=1.835000
probe at 240.000,240.000 is z=1.835000
probe at 240.000,40.000 is z=1.840000
probe at 240.000,40.000 is z=1.837500
probe at 240.000,40.000 is z=1.842500
Making the following gantry adjustments:
stepper_z = -0.020464
stepper_z1 = 0.008292
stepper_z2 = 0.007343
stepper_z3 = 0.004829