Tough call. Montero is a good C. Is he worth Garza or Peavy in a trade? I don't think so, no. I'd be tempted to send Floyd out though for Montero. You could also consider trading Slowey, who has struggled this year to show he is the Twins number 2 guy.
Floyd has been very solid for the most part lately, hold onto him. As k.k. said, Slowey is the first to go in a trade here. Aside from him, I don't see Montero matching the value of your other SP's.
And I don't think Montero is a huge upgrade at catcher to say the least. If that's all you can get, I'd try offering Slowey for Montero. Not really a big deal. See if you can really upgrade now.
Any decent C available in FA (post FA).
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Send Peavy! Maybe Im just a hater, but Peavy really isn't that good... He is a "name" pitcher. People know him for his name and think he is fantasy relevant. Id sell him for Montero.
He won't do the trade for Slowey, I was just listing the other pitchers for reference of the SP depth.
As for FA Catchers, there's minor upgrades available maybe but nothing special. Moves aren't free either so I don't want to keep adding/dropping searching for hot hand.
AJ Pier Paulino Soto (just got dropped, isn't getting the AB's) Treanor Kendal Lucroy Wieters
You could pick up Wieters and drop Pudge while also making the trade for Montero. He was a top 5 C coming into the year - he's worth the shot. I'd offer up any of those 3 pitchers you mentioned but would probably try Peavy first. It's no great loss no matter who you send away in my opinion