In the past I've used TP-Link TD-W8970 in similar situation (not miners, but a farm of computers for tests). The manufacturer has marked it end-of-life, I had hard time even finding the information. Other people used ASUS xDSL gateways, e.g. ASUS DSL-AC68U, but I don't know what was changed in the recent firmware.
Your best bet is probably:
1) convert your B.T. device to bridge mode and use a regular PC or Mac to share your connection.
2) buy an end-of-life Cisco IOS router (e.g. Cisco 1801 (ADSL over POTS), Cisco 1802 (ADSL over ISDN), Cisco 1841 + HWIC-1ADSL + HWIC-AP WLAN). They are now super cheap, but they aren't easy to set up, because they use Cisco's crown jewel IOS (Internetworking Operating System). On the flip side, there are plenty of sources to learn and get help. This is rock-solid industrial-grade solution for businesses and it was quite popular before VDSL or optical fiber pushed it out of the market.
Does B.T. charge you rental for your gateway or do you own it outright?
Also, are you sure that it is your router crashing&rebooting and not some line problems (real or artificially created). Where I used to live ISPs would remotely force customer's devices to reboot frequently to force them to upgrade to VDSL or fiber-optics. Do you know the noise margins and bit error rates on your line? I don't know the situation in the UK, but in many other countries ADSL was somewhat mired in political/financial problems on the provider side that made it hard to support for them.
Edit: Also, tell us how BT provides you with an IP address, is it via PPPoE, PPPoA, DHCP, L2TP, MER or something proprietary? This is very important!
Edit2: It was TD-W8970 or TD-W8980, just from the look of it. I recall returning TD-W8968 as it wasn't crashing, but it was just slow under load. Or it was TD-8961ND that I returned, again just from the look of it.
Edit3: I'll just cut&paste this from my gateway for my own reference, although we no longer have any xDSL where I live:
DSL line status
2.1 DSL link status
2.2 DSL synchronization mode
2.3 DSL last synchronization
2.4 DSL synchronization uptime 00 d 00 h 00 m 00 s
Rate and noise margin
2.5 DSL synchronization up Kb/s
2.6 DSL synchronization down Kb/s
2.7 noise margin down dB
Line quality (errors)
2.8 Errored seconds (ES) of downstream (since last synchronisation)
2.9 Severely errored seconds (SES) of downstream (since last synchronisation)