I'm not saying you are making things up, but that makes no sense to me. I don't think any Republicans I know are aware of that tactic, use that tactic, or would even think it's effective.
There's an well-sourced Wikipedia article covering the of “Democrat” as an adjective in place of “Democratic”, including its history and Republicans citing their justification for it: https://en.m.
wikipedia.org/wiki/Democrat_Party_(epithet)
> The term Democrat Party is an epithet for the Democratic Party of the United States,[2][3][4] used disparagingly by the party's opponents.[5] United Press International reported in August 1984 that the term had been employed "in recent years by some right-wing Republicans" because the party name implied that the Democrats were "the only true adherents of democracy."[6]...
> [Conservative] Political commentator William Safire wrote in 1993 that the Democrat of Democrat Party "does conveniently rhyme with autocrat, plutocrat, and worst of all, bureaucrat".[9]...
> Journalist Ruth Marcus stated that Republicans likely only continue to employ the term because Democrats dislike it,[2] and Hertzberg calls use of the term "a minor irritation" and also "the partisan equivalent of flashing a gang sign".[10]
That is just so...weak. I acknowledge the historical origins, but is anyone really bothered by this? "Democrat" is obviously a demonym for those in the Democratic Party, so shortening it to the "Democrat Party" (i.e. the party of the "Democrats") seems perfectly reasonable. I mean, it does lend itself to silly orthographic puns like "DemocRAT" etc., but by itself doesn't really seem particularly offensive.
Heck, before it was adopted as the name of the party, Democratic was also a disparaging epithet conjured by the faction’s opponents (though not one involving torturing grammar, because that's not how Federalists rolled.)
To be fair, Democracy had (up until that point) a rather tumultuous history.
And even in the modern day, it is often the case that self-styled "Democratic" institutions are measurably worse than their counterparts. For example, compare the "People's Democratic Republic of Korea" to South Korea, or the "Democratic Republic of Congo" to the mere "Republic of Congo".
