I would say it isn't the 305/35/24 tire size that is your issue as there are plenty out there running that size tire with zero rubbing when they're installed on the right rim with the right offset. Key being the offset, which is the issue with your wheel fitment and tire rubbing.
The higher the offset the closer the rim is to the inside of the fender and suspension components, the lower the offset the more the rim will stick out further from the fender lip away from the suspension components.
Most 24" rims that are meant to fit our vehicles fall in the +25mm to +31mm offset range (most being +30mm and +31mm), with your rims being +15mm offset that means that your rim sticks further out to the edge of the fender lip (maybe even past it in your case) and farther from the inside suspension components by 15mm (.59") more than the typical rim offset for our vehicles.
So when you add wheel spacers you are affectively lowering the offset of the rim, in your case your rims already have an offset that is too low for your vehicle, so wheel spacers will not help you there. Your rims are +15mm offset, add a 5mm wheel spacer and your new affective rim offset is +10mm, which is moving the wheel in the opposite direction that you need to solve your problem.
Some people do go through the process of milling down the back of the rim mounting pad to make minimal adjustments, affectively raising the offset of their rims. For example your rims are +15mm offset, shaving off 5mm of the rear wheel mounting face would net an affective rim offset of +20mm. This requires a highly skilled machine shop that is familiar with the process and has the equipment necessary to make sure the work is correct, even, and within tight tolerances. However, I've only heard of this being done to shave off single millimeter digits worth of material, not double digit 10+mm worth like you would need. This is because when you start milling away material to raise the offset of the rim you start adversely affecting the structural integrity of the rim. Sure 1-2 mm might be ok, but the amount that you would need I would venture to say is beyond the safety factors of the rim to remove safely.
Short answer, get new rims with the correct offset to fit your vehicle or raise your vehicle back up to stock height (and even that may not be high enough).
