Inversion Free Elliptic Curve Operations Is there a way (different than projective closure) to obtain inversion free elliptic curve addition formulas ?
Pick pretty much any projective coordinate system, and there is a plethora of inversion-free addition formulae.  For example, here's a library of inversion-free formulae for addition and doubling in short Weierstrass curves with $a = -3$, which covers all the NIST prime curves and many curves deployed for DH and signatures before Curve25519, using standard projective coordinates: https://hyperelliptic.org/EFD/g1p/auto-shortw-projective-3.html

However, if you want affine coordinates in the end, I don't think you're likely to find a way to avoid inversions altogether—at best you can put off inversions until the end and do only a small number of them, possibly only 1, depending on what you're doing.  E.g., $x$-restricted scalar multiplication on a Montgomery curve—as used by the X25519 Diffie–Hellman function—requires only one inversion at the end of the computation.