"Not once he would" vs. "not once would he"

Not being a native speaker and suffering semantic satiation from overthinking this, I'd like to ask this probably overly simple question.

Not once would he...

uses reversal for negation and means "he wouldn't even once..."

Not once he would...

is litotes for "He would frequently..."

Is that correct or did I mess up? If I did mess up, how to correctly express the two meanings?

Actually, whether the "not once" construct means "never" or "several times" might depend on the rest of the sentence – not just the order of "he would" or "would he". For example, there's nothing wrong with:

Not once would he strike out, but three times that game.

If you start with a certain kind of negative, you have to invert the auxiliary:

• Not often does he come this way.
• Never would we call them after eight o’clock.
• Seldom do the bells ring so long as they did that day.
• Hardly had he put on his boots when his seat gave way.
• Never shall I pass this way again.
• Rarely do we see the likes of them in these parts.

Or, as taken from a particular Tale:

• Not until then did they notice that Gandalf was missing.
• No sooner did Tom see Balin come into the light than he gave an awful howl.
• Nothing wholesome could they see growing in the woods, only funguses and herbs with pale leaves and unpleasant smell.
• Not for a long while did they stop, and by that time they must have been right down in the very mountain’s heart.
• Not in a thousand years should I forget the ways of this palace.
• Never again will I have dealings with any wizard or his friends.
• Never before had any man mounted him, but I took him and I tamed him, and so speedily he bore me that I reached the Shire when Frodo was on the Barrow-downs, though I set out from Rohan only when he set out from Hobbiton.
• No folk could they see, nor hear any feet upon the paths; but there were many voices, about them, and in the air above.
• Not once did they feel the sense of present evil that had assailed them before the attack in the dell.
• ‘Seldom in my life has any boat come out of the North, and the Orcs prowl on the east-shore,’ said Boromir.
• Not till the spring comes and the new green opens do they fall, and then the boughs are laden with yellow flowers; and the floor of the wood is golden, and golden is the roof, and its pillars are of silver, for the bark of the trees is smooth and grey.
• ‘Not idly do the leaves of Lórien fall,’ said Aragorn.
• Seldom has any lord of Rohan received three such guests.
• No counsel have I to give to those that despair.
• Never again shall it be said, Gandalf, that you come only with grief!
• Not yet does my road lie southward to your bright streams.
• Seldom had he remembered it on the road, until they came to Morgul Vale, and never had he used it for fear of its revealing light.
• Never yet had any fly escaped from Shelob’s webs, and the greater now was her rage and hunger.
• Hardly had Sam hidden the light of the star-glass when she came.
• Never in all my life had I met them, until we came to Pelargir, and there I heard them crying in the air as we rode to the battle of the ships.
• Not in half a thousand years have they forgotten their grievance that the lords of Gondor gave the Mark to Eorl the Young and made alliance with him.
• No peace shall I have again under beech or under elm.
• Never shall that line fail, though the years may lengthen beyond count.
• Not too soon came their aid to the Rohirrim; for fortune had turned against Éomer, and his fury had betrayed him.
• Not for naught does Mordor fear him.
• Hardly has our strength sufficed to beat off the first great assault.
• ‘No longer do I desire to be a queen,’ she said.

"Not once he would" is not a familiar construction in English. I think it would be expressed "Frequently he would..." or something similar.