The Virgo and A1795 clusters of galaxies were reobserved by the Extreme Ultraviolet Explorer with in situ background measurements by pointing at small offsets. Earlier, a similar reobservational strategy applied to the cluster A2199 revealed that the background radial profile was consistent with a flat distribution, and therefore the original method of extracting cluster EUV signals by the subtraction of an asymptotically determined background was valid. It is shown here that the same conclusions hold for the current sample. A model of the background was obtained from its known properties and the in situ measurements, and the subtracted cluster fluxes remain in agreement with those reported in our discovery papers. They are also consistent with results from the most conservative procedure of direct point-to-point subtraction of the in situ background and proper error propagation, which still preserves the existence of the EUV excess and its rising radial trend. We present evidence that argues against the soft excess as due to peculiarities in the line-of-sight Galactic absorption. The data appear to favor a thermal origin of the emission.