Can capital still be paid its marginal product in the absence of a homogeneous capital stock?
Nothing about marginal productivity theory depends on the exact truth of a simple aggregate production function with capital defined by a single number

Different sorts of capital used as separate production technologies prevent clean aggregation to a representative form of capital but does not prevent capital from being paid its marginal product.

To make things simple, consider an economy with two kinds of capital $k_1$ and $k_2$ and no labor. There is only a single final good ($y$) but are two separate production technologies $y_1$ and $y_2$ where $y_1 =  k_{1}^{\alpha_1}$ and $y_2 =  k_{2}^{\alpha_2}$. Then aggregate production of $y$ is:
$$y =  k_{1}^{\alpha_1} + k_{2}^{\alpha_2}$$
If $0 &lt; \alpha_1 &lt; \alpha_2 &lt; 1$ then for positive rental rates on capital $r_1$ and $r_2$ it will be efficient to choose a positive amount of both types of capital such that for each type $i$: 
$$ \alpha_i \cdot k_{i}^{\alpha_i - 1} = r_i\Rightarrow k_{i}^{*} = (r_i/\alpha_i)^{1/(\alpha_i - 1)} $$

There is no single $k$ that represents capital in this economy. Sure you could define $k=k_1 + k_2$, but that wouldn't mean exactly the same thing. On the margin the two sorts of capital don't have the same product and so aggregation doesn't make sense here. But in this setting, it is likely that the rental rate on capital would be equated ($r_1 = r_2$) because why would you buy one sort of capital when the other sort paid more?