My home network setup - please evaluate and advise

I got 300mb (up)/50mb (down) fibre into my house a few weeks ago. I have a two story house with 3 bedrooms upstairs and 3 rooms downstairs ... typical small family home.

For various reasons the router (Huawei HG659b) went upstairs in the main bedroom, and is currently placed on top of the wardrobe in the corner of the room. I have a Google mesh https://store.google.com/product/google_wifi attached to the router, and another Google mesh downstairs in the living room which is directly below the main bedroom. Wireless tests close to the router show that I'm getting full speeds, but this degrades dramatically when I move outside the main bedroom.

I thought that this setup would be enough to get decent wireless signal around the whole house, but apparently not. When I run tests on the Google mesh (through the app) the mesh gives a result of "weak" or "fail" around 50% of the time (shows a speed of 15-20mbps). The other 50% of the time the mesh test shows "great!" with a speed of 120mbps.

I've tried moving the mesh units around a bit (not a huge amount), but it makes no difference to results.

I have an Nvidia Shield (Plex, gaming etc) downstairs which is stuttering when connected to the mesh network. I did try to connect to the 5g wireless signal, but this doesn't always reach downstairs. The 2.5g wireless signal is too slow at about 5mbps.

Moving the router downstairs or hard wiring is not an option at the moment. I'm a bit stunned that my wifi in a reasonably small house is so poor. I'm also very disappointed that the Google mesh system seemingly cant reach from the bedroom to the living room directly below.

If anyone has any advice I'd greatly appreciate it. I'm using the cat5 cables that came with the hardware. Would it make any difference to replace with better (maybe cat6??) cables? What else could I do to improve things? Another Google mesh? As I've said previously, moving the router or hard wiring not an option at the moment.

I'm a noob at this so maybe doing something stupid. Any advice greatly appreciated.

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/edit/ I can upgrade to gigabit speeds ... would this solve my problems? Would upgrading the router be an option (not sure if my isp allows this?)