"...to try to..."
FOTR
"I am afraid we shall have to try to get one pony at least."
He knew of nothing that would prevent them from crossing as easily as he had done; and he felt that it was useless to try to escape over the long uncertain path from the Ford to the edge of Rivendell, if once the Riders crossed.
TTT
(none)
ROTK
Though if an enemy were so rash as to try to enter that land secretly, then it was also a last unsleeping guard against any that might pass the vigilance of Morgul and of Shelob.
"...to try and..."
FOTR
"Why, this is the Stock-brook!" said Pippin. "If we are going to try and get back on to our course, we must cross at once and bear right."
"I was thinking so," said Frodo. "But we have got to try and get there; and it won’t be done by sitting and thinking."
"Not far from this tunnel there is, or was for a long time, the beginning of quite a broad path leading to the Bonfire Glade, and then on more or less in our direction, east and a little north. That is the path I am going to try and find."
"I am not going to try and guess," said Frodo smiling.
"It would have been useless in any case to try and win over the honest Radagast to treachery."
"I could think of nothing to do but to try and put a shutting-spell on the door."
"We might make him useful. But if I cannot, we shall have to try and lose him. He is very dangerous."
TTT
"The oldest were planted by the Ents to try and please the Entwives; but they looked at them and smiled and said that they knew where whiter blossom and richer fruit were growing."
"And if we’re going to try and get down, we had better try at once. It’s getting dark early. I think there’s a storm coming."
"It isn’t funny, O no! Not amusing. It’s not sense to try and get into Mordor at all. But if master says I must go or I will go, then he must try some way."
"Do not tie their hands. They will give their word not to try and see."
ROTK
It was not enough for him to find his master, he had still to try and save him.
"He’s a prisoner in Bag End now, I expect, and very frightened. We ought to try and rescue him."
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I'm not sure about any specific patterns, but I did notice that of the "to try to" instances, only one is spoken by a character, whereas with "to try and", all are spoken except one instance.