You already know how a Terralux TLE-310M performs.
Matt Smith (a member here and owner of AdventureSportFlashlights) did a video review of some maglite drop-ins which included the Terralux TLE-310M which you already have, in this video at around 5:50 he provides output and beam distance measurements:
According to Matt the beam distance for the Terralux is 261m, which is about 17kcd. Using this as a reference point there are many lights within your budget that have a greater beam distance, it’s just a case of finding one that matches all your requirements.
Do you want to stay with NiMH batteries or do you want to move to Li-ION batteries?
The C8 you mention will require Li-ION bin it’s standard form but is capable of a much greater beam distance and is very easy to modify, or you can buy a host and choose your own driver and LED to install.
If you look at the 4th and 5th pictures in this review (of a C8+ but the same applies to a C8):
https://budgetlightforum.com/t/-/52774
you can see how the torch breaks down into it’s parts and how easy it is to access the internals. And while you can buy a remote switch for it you can easily access the switchboard and switch to connect an external switch yourself, and while i haven’t done it should be possible to power the head from an external NiMH battery pack if you don’t want to use Li-ION as long as you match the voltage to the driver, but the C8 is only one option and there may be a more suitable NiMH ready option if you decide this.
Another cheap option might be to replace the LEDs in the Terralux - if the LEDs are on their own accessible MCPCB and you are willing to try a reflow 