Consider having an access point running in bridge mode for those devices at the back end. Even a high gain router may not mean better connection at the back as each client needs its own high gain adapter which is costly. There are a number of options (WDS or wireless bridge) if you do not run cable from your primary router. WDS allows 'roaming' between the stronger signal router however at a cost of half the bandwidth. With 50Mbps you will not notice this.

Couple of points.

1. Is the present router working enough to keep you reasonably ok, forget about the wireless range for the moment? Say for clients connected near it?
2. If the answer to (1) above is true, then invest in a wireless range extender, many options are available depending on your budget.
3. Are you going to stay with Asus or consider other vendors? Some wireless extender/bridge/whatever to extend the range may be vendor proprietary so choose a vendor with good firmware and hardware support. A good router will NOT need a scheduled reboot and will run without issues for years rebooting only after a power failure.

Likely even with a high end expensive router the 5Ghz signal at your back room will have, if you are lucky, one bar signal. On 2.4Ghz its going to get interference from neighbours' wifi, your microwave and cordless phones. That is why mesh networks are coming onto the market to solve these issues but its too early to get them as (1) expensive (2) firmware are more like alpha builds (3) new technology

For many years had used the TM supplied router as a VLAN switch and had multiple routers handling wifi using a single SSID and devices auto connect the optimal access point (including one connected to the router LAN port to handle wifi as the wifi on TM router was not robust enough). These were hardware carried over from pre-streamyx and the routers (AirPort) got replaced every 8 to 10 years as the technology render them ineffective (first ones were b/g capable).

On average, the 5GHz (non AC older devices as old as ones purchased in 2010) typically get almost 300M speeds and 2.4GHz devices typically 70-100M speeds or better (and this is like consistent stable numbers for years). When you mention 20-30M speeds its likely wireless interference from surrounding 2.4GHz wifi networks (assuming you are looking at router logs to see actual speed and not internet speed test which adds a lot more variables). Device disconnections probably from interference.

When you invest in a new router, try in your mind to think of it in two parts,

1. Connecting to TM modem and as a VLAN switch.
2. Wifi and devices need to have 5GHz connectivity

On wifi, that is where things get complicated. Its likely you will need another access point (whatever tech) to get good signal strength at the back simply because there are regulations on how much max power a router can transmit.

A bit of configuration with Mikrotik/UNBT as a VLAN router and with a LAN cable move the existing router (as an AP) to mid point could be the cheapest solution. He needs to test how stable his existing router is in AP mode. Guess is its probably going to function a lot more stable without the heavy lifting required for routing.