Accurate measurements of the geometric shape and the internal structure of cultural artifacts are of great importance for the analysis and understanding of artworks such as paintings. Often their complex layers, delicate materials, high value and uniqueness preclude all but the sparsest sample-based measurements (microtomy or embedding of small chips of paint). In the last decade, optical coherence tomography (OCT) has enabled dense point-wise measurements of layered surfaces to create 3D images with axial resolutions at micron scales. Commercial OCT systems at biologically-useful wavelengths (900 nm to 1.3 µm) can reveal some painting layers, strong scattering and absorption at these wavelengths severely limits the penetration depth. While Fourier-domain methods increase measurement speed and eliminate moving parts, they also reduce signal-to-noise ratios and increase equipment costs. In this paper, we present an improved lower-cost time-domain OCT (TD-OCT) system for deeper, high-resolution 3D imaging of painting layers. Assembled entirely from recently-available commercially-made parts, its 2x2 fused fiber-optic coupler forms an interferometer without a delicate, manually-aligned beam-splitter, its low-cost broadband Q-switched super-continuum laser source supplies 20 KHz 0.4-2.4 µm coherent pulses that penetrate deeply into the sample matrix, and its single low-cost InGaAs amplified photodetector replaces the sensitive spectroscopic camera required by Fourier domain OCT (FD-OCT) systems. Our fiber and filter choices operate at 2.0±0.2 µm wavelengths, as these may later help us characterize scattering and absorption characteristics, and yield axial resolution of about 4.85 µm, surprisingly close to the theoretical maximum of 4.41 µm. We show that despite the moving parts that make TD-OCT measurements more time-consuming, replacing the spectroscopic camera required by FD-OCT with a single-pixel detector offers strong advantages. This detector measures interference power at all wavelengths simultaneously, but at a single depth, enabling the system to reach its axial resolution limits by simply using more time to acquire more samples per A-scan. We characterize the system performance using material samples that match real works of art. Our system provides an economical and practical way to improve 3D imaging performance for cultural heritage applications in terms of penetration, resolution, and dynamic range.