I appreciate you comments--thank you.

Good advice. I'll ask both the $175 guy and the $1,400-$4,000 guy exactly
what they would do. Both these guys work for chimney repair companies and
aren't handy-men. But the $175 guy is also pushing the $2,500 liner in a
really hard-sell way and that's put me off. Yes, the bricks are definitely
loose and I can pull them out by hand (and I have). But for an area so
small my gut-feeling was that this shouldn't be a multi-thousand dollar
job. It's not like I want the chimney floor in gold leaf. Up to $4,000
for just a brick and mortar job? Ay-yi-yi.

Well, I'm a new homeowner (well, almost four years now) so there's always
something to learn.

Thanks again!

David
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Someone has to look inside the chimney to see what is going on and if
a liner is needed. If loose you mean you can move them then its bad.
175 , if he removes them , cleans and remortars them then ok, if he is
just pushing in a 1/4" of mortar than no. Not knowing how many and how
bad who can say. The 175 is probably a handyman doing it in a day he
figures, but he may not understand how bad it really is. 1400-4000 may
be the other extreme. You need more bids and to learn what is really
going on. Get a guy to look in the chimney and photograph the issues,
get bids.