A dry patch or an oiled patch at the end will normally remove or neutralize enough of the residual ammonia to prevent problems.
One solvent you should NEVER use in conjunction with a high-ammonia solvent is Shooter's Choice. The ingredients in SC will combine with the ammonia and form a chemical that WILL etch and damage your barrel. But I've not read any cautionary notes about any other solvent/ammonia mix.
Here's an good article about barrel cleaning:
LINK