hi! i'm a year 13 taking further maths and i really think that with the options you have in mind, further maths (at least to as level) would be a huge asset to your application, whether you go down the econ or the maths route. i wouldn't worry too much about your performance in the maths challenge as that is testing a very specific type of maths that isn't necessarily an indicator of ability at university level. i never was great with the olympiad-type maths and am predicted A*A* in maths and further maths, if that's any reassurance to you 😀 a much better indicator would be, when you've covered a bit more content, seeing how you do in STEP/MAT papers
first off, ask your school and see what support they can give you. of course, joining the class would be ideal, and even if you've missed out on a lot of content so far, you'd have to catch up either way if you were to self-study so that shouldn't be a reason for them not to let you take fm. if timetabling doesn't work out, at least try to see if they can give you assessments and such to try to get a predicted grade for it; even if all you do is turn in exams to the teachers, that's at least some kind of structure to your learning that hopefully would be reassuring
if you go down the self-study route, i would recommend looking at
the amsp as they support state school students in a position like you. edexcel would be my recommendation of exam board as they have the largest resources imo - though if your school do a different board it may be better to match what they do to get the most support from them that you can. it also would be better to match their optional modules if you can
i'd be more than happy to help if there's anything specific about further maths that you want to know 🙂 best of luck, i really hope this works out for you