how you could find some other ways to prevent NATO expansion into Eastern Europe?
"The Slovak way" - Slovakia was not invited to the first round of expansion, because of less than democratic tendencies of the government. Mečiar was not called the Slovak Lukashenko for nothing, though he (fortunately) failed to rule the mass media and to consolidate his power. And he very much wanted the membership, to legitimize his image. His rhetoric turned pro-Russian only when his government was very explilcitely mentioned as the reason for the exclusion of Slovakia.
The issue is, you can easily create a similar problem[*] in almost any CE and EE country, but it is going to be a bleak timeline if happens for the majority of them. And in that case, NATO might expand anyway, to keep the influence, turning a blind eye if necessary (see Turkey).
[*] Poland turns nationalistic and ultra-religious. Yugoslavia war engulfs Slovenia. Transnistria-like separatism in Latvia. Bulgaria and Romania under single-person dictatorship. Politically unstable Czech Republic after several failed elections strangles the economy during the worst possible time. OTOH, if Hungary goes dictatorial and nationalistic, all the neighbouring countries will beg for being admitted to the NATO.