I am unsure why you chose such rarely used phrases.
There is a long list of words that are not modifiable: perfect, flabbergasted, worthless to name a few ("few" is modifiable).
As for "me thinks" (as two words or one), I haven't heard anyone use that term to begin, end or modify a sentence. What do you think of "I reckon?"
And speaking of strange words which are only modified, when is the last time you have heard of someone being "gruntled," a flag or banner being "furled" (methinks there is a famous poem that uses that term from the 1800's, I reckon). And outside of a newspaper when is you heard that someone is embattled.