Avoiding the Old Forest...?

[Kuruharan]

they anticipated no real difficulty in getting through the Forest

Speaking strictly within the confines of the story I agree with this to a large extent, although Merry at least had some ideas that the Old Forest was more dangerous than your typical wood.

It doesn't even seem that any other idea besides plowing right through the wood was considered.

[Bêthberry]

In A Conspiracy Unmasked, Frodo explains that he wants his departure to remain secret for at least a few days, so he suggests going where none would expect a hobbit to go.

Originally Posted by the discussion, ACM

". . . The only thing to do is to go off in a quite unexpected direction." [says Frodo]

"But that can only mean going into the Old Forest!" said Fredegar horrified. "You can't be thinking of doing that. It is quite as dangerous as Black Riders."

"Not quite," said Merry. "It sounds very desperate, but I believe Frodo is right. It is the only way of getting off without being followed at once. With luck we might get a considerable start."

Fredegar's response following this adequately sums up what Tolkien wants the reader to know, that most hobbits are deeply suspicious and afraid of the Old Forest, so none would think, even under pressure from the Black Riders, to suggest that Frodo might have gone through the Old Forest.

In other words, they take the least likely route. Interestingly, no one mentions if the Old Forest would be malevolent to those who seek them.

[Tuor in Gondolin]

If they stay in the clearing it's quite conceivable
the Black Riders would break in and quickly overtake
them (or come the other way going around and then south
after going past the High Hedge) whereas that's impossible
for horses in the Old Forest. And if you look at the maps by
Strachey or Forstad (if the former is still in print) if you
assume the Old Forest is navigable it's pretty much a
covered, straight path to Bree.

Btw, a possible plot hole is the Bucklanders apparently
being totally unaware (unless I forget references in LOTR)
of Tom Bombadil, especially since he must have been not
infrequently in the eastern Shire rapping with Farmer Maggot
since I can't see Maggot's wife letting him traipse off to some
foreign place across the Brandywine.

[Inziladun]

Originally Posted by Tuor in Gondolin

Btw, a possible plot hole is the Bucklanders apparently
being totally unaware (unless I forget references in LOTR)
of Tom Bombadil, especially since he must have been not
infrequently in the eastern Shire rapping with Farmer Maggot
since I can't see Maggot's wife letting him traipse off to some
foreign place across the Brandywine.

Well, I don't know if Bombadil had set foot in the Shire within living memory of any of the Hobbits. His 'country' seems to have consisted only of the Forest and the Downs; and Gandalf (and Tom himself) stated he did not leave the bounds he had set for himself for any reason.
I think it more likely Maggot visited him, especially since Merry noted that he had been known to enter the Forest at one time.

[Rumil]

Tom seems to have had the odd Shire-wards excursion...

Maggot's sons bowed at the door, his daughters did their curtsy,
his wife brought tankards out for those that might be thirsty.
Songs they had and merry tales, the supping and the dancing;
Goodman Maggot there for all his belt was prancing,
Tom did a hornpipe when he was not quaffing,
daughters did the Springle-ring, goodwife did the laughing.

though admittedly he didn't get such a good reception at Grindwall..

'Hoy! Here's Woodman Tom with his billy-beard on!'
laughed all the little folk of Hays-end and Breredon.
'Ware, Tom! We'll shoot you dead with our bows and arrows!
We don't let Forest-folk nor bogies from the Barrows
cross over Brandywine by cockle-boat nor ferry'.
'Fie, little fatbellies! Don't ye make so merry!'

[Inziladun]

That would certainly seem to put ice on my theory, but I was drawing strictly from LOTR.