Affordable Bass Amp for drop G

I have an Epiphone Thunderbird IV Pro tuned to G0 D1 G1 C1 (Drop G), with the Rotosound RS66LH+ string set (gauges 175, 135, 105, and 85).

What I'm planning on playing with it involves progressive metal, brutal death metal/slam, goregrind - that kind of stuff. Although great clarity isn't a major requirement (as I want it to feel somewhat muddy), I don't want it to just come out as low fuzzy noise.

I was thinking of getting an affordable amp that really captures the low end, but couldn't find many reliable examples - the Fender Rumble 15 v3 was the only one that appeared a possibility.

I'm on quite a tight budget, so something below £300 would be great! Any recommendations?

 

I'll most likely only use overdrive with mid-to-high gain and contour, as I want the bass to stay in the mix and not get drowned out by the guitars. I guess for the higher two strings, I'd want them to be punchier and more mid-range (to stand out), and for the lower two strings, I'd want them to be more bass-heavy to strengthen and thicken the lower guitar notes.
I see what you mean about the muddy/low fuzz - I mean so the the notes can be distinguishable, but so the frequencies have a slight dissonance to them.

 

I'd go for more the bass holding its own part. Rather than being the low rumble backing up the frequencies, I meant the bass would be distinguishable from the guitars, but the notes would harmonise to create a thicker overall sound.