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Among log canonical surface singularities, the ones which have a rationalhomology disk smoothing are the cyclic quotient singularities$\frac{1}{n^2}(1,na-1)$ with gcd$(a,n)=1$, and three distinguished ellipticquotient singularities. We show the existence of smoothable KSBA normalsurfaces with $\pi_1=1$, $p_g=0$, and $K^2=1,2$ for each of these threesingularities. We also give a list of new (and old) normal surfacesingularities in smoothable KSBA surfaces for invariants $\pi_1=1$, $p_g=0$,and $K^2=1,2,3,4$.

KSBA surfaces with elliptic quotient singularities, $\pi_1=1$, $p_g=0$, and $K^2=1,2$