Look like as above twin 11" standard 109. Your pic has them fitted the correct way. [ I once bought a 109 that pulled to the right going forward and hard left in reverse! Turned out some idiot had fitted right hand back plates both sideso_O. Common mod was/is to change pipe work to have bleed...
There are some who say they have replaced springs through the top of the box. I did one once, not easy.
Given the other issues and you are managing without I say no. To be back in full working order time for a box out overhaul.
If good and patient with changes it can keep going some time, you look to have the remains of all 3 springs I think. Syncro hub is an early design from the 30's, works well enough but springs are a weak point.
The second gear jumping out [ on over run?] is likely not related and is wear and...
A jiggle job, free off nuts at manifold, get all three bolts in the next joint in but loose, free bracket clamp above axle and clamp at tail pipe.
Starting at manifold move towards engine some to set in right position., do nuts up equally and so on.
The box itself is a pretty basic item, Overhaul kit available. It is just that the steering column has to come out with it, not so bad with 2/2A as no dash in the way. Series 3 more work.
Your float could be down to worn out dampers/shocks, other possible is worn bushings/brackets in rear axle.
How much lift did it have? If more than 2 inch likely shocks will be overlength and not compress enough now.
SWB are fine without anti roll bar [ mine does not ] with suspension in good...