Broken Reverse gear?

Ok so for a while now (3 months) it has been really hard to get into reverse like you try to put it in and it feels like there is something blocking it because it will go only half way into reverse.. and then I have to double clutch a bunch and keep trying till it goes in. So I took it to a shop and they did an 'inspection' and said that my reverse syncrhos are worn out and I'd either need to get a whole new gear box or redo my fourth gear synchros.

So I said ok yeah whatever cause a both of the options are $1500 and I've recently noticed I can't get the car into 5th gear when stopped or going less than 40 m.p.h at all like just won't go in no matter what but when you pass 40 m.p.h. it'll go in just fine. I feel like my gearbox is almost like shifted or something so that 5th and reverse are effective cause all my other gears are great.

Btw, this a very reputable shop and it is a 2004 Hyundai elantra which means xd2 I believe.
I just don't know if I should spend all this money if it is a different or easier fix. Oh and my clutch was done 10k miles ago.