How to accurately model wideband RF reflections?
So, to give you something to read up on first, the channel you describe is a Rician or Rayleigh channel, depending on whether you have a dominant line-of-sight path or not.

So, as a first approach, to delay something in time, you don't have to shift it by a whole sample – you can also do it in frequency domain, by DFT'ing your signal, multiplying it with a $e^{j\frac{\Delta t}{f_s} f}$, and then IDFT it back. That's how I've built all my radar simulations.


  I'm assuming that each reflector can be modeled by the distance to the transmitter and the receiver, and some real-valued attenuation constant.


A radar target typically also phase-shifts the electromagnetic wave – on perpendicularly hitting a metal surface, by 180°, but differently for more complex surfaces. In reality, we often model that stochastically. What is appropriate for you will very much depend on what you simulate. A model for scattering of reflections e.g. on leaves will not be very useful for modeling reflections e.g. inside an oil tank, and vice versa. Both are use cases for radar.

For many scenarios, there's "standard" models, such as the COST-Hata urban model, the ITU indoor models and many, many more. It really depends on which environment you're considering, and also, which group of researchers you ask.

Many of these models are defined for what I call the "easy RF" ranges below ~5.8 GHz. Since radar, for Doppler and wavelength reasons, often operates above, things often aren't too well represented by these models (i.e. they simply don't apply to common radar frequencies > 8GHz). This has two interesting aspects:


The higher your frequency, the more quasi-optical your models get for most useful spatial scales, and
Since millimeter waves are very en vogue right now (with all the 5G research going on), you might find very interesting RF propagation models when looking at very recent papers. As an example for a very practical, hands-on-testing based propagation/reflection description, try Simić, Perpinias and Petrova: 60 GHz Outdoor Urban Measurement Study
of the Feasibility of Multi-Gbps
mm-Wave Cellular Networks. Downside of these considerations is always that, albeit multipath does play an important role for these researchers, the individual phase really doesn't matter (only the interference with other paths does).