Hello Gustave and Welcome,

I've got a few suggestions that might help you.

#1 Don't waste money and time epoxying the whole bed it's not required, Just do the rails. You will 99.9% of the time have a spoil board on the machine which you will surface flat and parallel. So all you need is a baseboard that is flat, uniform in thickness, and stable ie: Not MDF.

If you are using Tig welder then distortion from heat will be much lower than Mig and you can control movement better. Take your time and move around so heat is spread around the frame.

#2 Use HGW on X & Y as they provide more stability. I would even use them on the Z-axis but I realize you are trying to keep the width to a minimum. 20mm rails will be fine on all axis.

( you mentioned HGR as though it was a bearing, HGR is the rail, HGH and HGW are bearing types.)

#3 The Z-axis bearings are spaced a little too close together and I would spread them out a little to improve stability. Even if this meant increasing the rail and rear plate length.

#4 Go with 25mm ball Screws for the long axis but use 25mm pitch not 10mm with a 2:1 ratio. This will half the screw speed and reduce any chance of whip. With the ratio, It will give the equivalent of 12.5mm pitch so a little higher feed rate but much lower screw speed.

20mm Screw with 20mm pitch with 2:1 for the Gantry axis. I know you have drawn it directly coupled but I would change that to belt drive for a few reasons.
It allows for the ratio to half the screw speed and it lowers resonance greatly which helps the stepper motors run much smoother. It also helps with servo's for similar reasons too but not to the same degree.

You didn't mention the motors your using, but if Servo's with 3000 Rpm then you may want to use a 3:1 ratio.

#5 Use Fixed BK bearings on Both ends of the Long screw as they offer a little more stiffness.

#6 You won't have any issues with racking at this width with this design unless you want to take very heavy cuts at the outer edges and even then it won't stall the machine, at worst you get a little deflection which doesn't really matter when roughing or hogging out material.

#7 Lastly, Buy a good large Square. This will help you set up the Gantry and Z-axis. My preference is a Granite triangle.
Don't stress over trying to achieve 0.001 precision for a wood router because it's just wasted as the material will move more than that. So what I'm saying is don't be paying Big money for precision instruments that you will never take full advantage of.

Hope this helps and good luck.