The idea of improvement that could have been brought to Principla Mathematica [PM] is quite misplaced! Replacing the primitive team {INCLUSIVE-OR, NEGATION} by Sheffer's (actually Peirce's or even... Chrysippus'!) NAND wouldn't have improved PM, at all.
Because, primo, PM is a piece of kindergaten charabia that should not have been written -- and published -- in the first place: it is nothing but an elementary exercise in formalisation (a rather long one, indeed). As a matter of fact, one can generate it with the help of appropriate software.
Even the idea of formalisation in PM is besides the point: in PM, like in Frege's Begriffsschrift (1879) or in his Grundesetze der Arithmetic (1893--1903) and in Peirce's pioneering 1885-paper, the formalisation concerns only a superficial aspect of logic, namely the (provable) formulas as expressing propositions and / or propositional schemes, not the proofs themselves: the concept of proof -- the central concept of logic, after all -- is left un-formalised in PM. [*]
Second, the handling of quantification (first- and second-order) in PM is seriously flawed and constitutes a considerable step backwards even with respect to Frege. (This is, by the way, one of Goedel's side remarks on Russell, not mine. Cf. Goedel's Russell's mathematical logic, in The Philosophy of Bertrand Russell, edited by Paul Arthur Schilpp, Northwestern University, Evanston and Chicago IL 1944, pp. 123--153.)
Third, the Russellian finding, meant to avoid paradoxes and the like -- namely the so-called ramified theory of types -- is a paradigmatic piece of muddy thinking: in PM, the so-called orders and the type hierarchy are introduced only in order to get rid of them, at a later stage (by the so-called Reducibility Axiom).
Fourth, the actual mathematics `formalised' (so to speak, i.e. in formularian terms) in PM is rather elementary.
Finally, PM (actually Russell and Whitehead) has done more damage than good to the reasearch in (theoretical) logic, during the last hundred years or so.
[*] The proof themselves have been first formalised by Nicolaas Gerrit de Bruijn and his students and collaborators at the Eindhoven Polytechnics (NL), about 40 years ago, within the Automath project (Automated Mathematics), since around 1967--1968. Cf., e.g., https://www.win.tue.nl/automath/ and my Abstract Automath, Mathematical Centre, Amsterdam 1982 [Mathematisch Centrum Tract 160] @ https://www.win.tue.nl/automath/archive/webversion/xaut021/xaut021.html.