Hi, welcome to ATARNotes!
Doing 3 3/4s in Year 11 is pretty rare, but if you are willing to put in the time and effort, I think you will be fine. Since you said you don't wish to do general 1/2, I think it may be good for you to do Further 3/4 in year 11. That saying, you said your year 10 extended maths is harder than Further, so do you mean you cover a lot of methods content as well in this subject? Methods and Further cover completely different areas, so what I'm trying to say is if your year 10 maths subject covered more Methods than Further content, it's definitely wise to learn/consolidate some Further 3/4 content over the holidays, especially since you mentioned that you were 'not passing with flying colours.' Further 3/4 is more straightforward than Methods, but it is definitely not an easy subject (especially when it comes to financial maths and geometry), so you need to have a really solid maths foundation to do well (as in get a 40+).
I'm also a bit curious to the fact that you said you needed to do general 1/2 first if you chose to do Further Maths in Year 12? Is that your school's compulsory requirement if you choose to not accelerate in Further Maths? Because I know in a fair few schools they allow students to pick Further Maths in Year 12 without doing general 1/2. But as you mentioned before, even if your school allows this option, it will mean you have a year of not doing maths, which is not ideal.
I can definitely appreciate your need to take a maths subject, despite hating it. So I think doing Further 3/4 in Year 11 may be good in the sense that you truly get a taste of doing a maths subject designed by VCAA rather than designed by the school. This can be quite good. Maths subjects designed by the school can be rather tedious and dry, but when I did Further for instance, I felt the subject was quite interesting and offered a new perspective with regards to learning maths. That saying, if you find you still hate maths when you start doing Further, you could possibly drop it (not sure if your school allows you to drop a 3/4 subject). In my experience, if you 'hate' a subject (like the subject's not really for you), you end up learning very little and perform poorly. Personally I don't feel its worthwhile to invest time in a subject that's not a prerequisite and you really don't enjoy, because all it does is eat up your time and motivation where it could negatively impact your other subjects.