The ongoing development of intense high-harmonic generation (HHG) sources has recently enabled highly non-linear ionization of atoms by the absorption of at least 10 extreme-ultraviolet (XUV) photons within a single atom (Senfftleben et al, arXiv:1911.01375). Here we investigate how the generation of these very intense HHG pulses in our 18-m-long beamline is aided by the reshaping of the fundamental, few-cycle, near-infrared (NIR) driving laser within a 30-cm-long HHG Xe medium. Using an incident NIR intensity that is higher than what is required for phase-matched HHG, signatures of reshaping are found by measuring the NIR blueshift and the fluorescence from the HHG medium along the propagation axis. These results are well reproduced by numerical calculations that show temporal compression of the NIR pulses in the HHG medium. The simulations predict that after refocusing an XUV beam waist radius of 320 nm and a clean attosecond pulse train can be obtained in the focal plane, with an estimated XUV peak intensity of 9 × 1015 W cm−2. Our results show that XUV intensities that were previously only available at large-scale facilities can now be obtained using moderately powerful table-top light sources.