TA's a very good source.
"Americanism" is deficient because it seems to create in its adherents two distinct problems: indifferentism, and moral relativity.
The form of Gummint is not really the problem--it's the fact that "Americanists" lose sight of First Things, allowing judicial rulings to substitute for moral verities.
The democratic republic, per se, is not objectionable so long as it maintains a Judaeo/Christian understanding of foundational principles.
Depends how it came about. I would maintain that a republic is objectionable if it owes its existence to the disestablishment of a monarchy (which arguably excludes your conditions, in which case we would be in agreement). This does not apply to the US since the rebellion of 1776 did not interfere with George III's position as King of Great Britain. However, the current republican governments of France, Portugal, Austria, Hungary, Germany, Italy, etc. most certainly are objectionable, and would continue to be so even if they attempted to bring their laws more in line with Judaeo-Christian morality.