A training captain once uttered the following words to me, and they have stuck ever since - "...once that happens, all bets are off"
In your situation, you have already diverted and fuel is tight - the approach you briefed has just gone out the window.
Still have time? Get PNF to check the perf and adjust (bodge...) the timing, ROD and outbound track (terrain permitting).
If you pull it all together, you should be in a good position to make a visual at or before minimums. If you really are tight on fuel, you might have to keep it going with the RA as a reference to terrain. [I know how crazy that sounds - but remember, if its that bad "all bets are off".
The only thing guaranteed, you are coming down! One way or the other