What's a positive phrase to say that I quoted something not word by word

Paraphrase is the perfect word.

To paraphrase Churchill, we will fight them everywhere.

Or

Paraphrasing Churchill, we will fight them everywhere.

There are plenty of examples at Lexico.

Or, less formally, you could use gist:

He said, "We will fight them everywhere." That, at least, was his gist.

Or

He said, "We'll fight them all over the place," or words to that effect.

Paraphrase is perfectly good here, and probably the most natural choice in most written contexts e.g.

Paraphrasing Oscar Wilde, "truth isn't pure or simple"

You could also caveat the word "quote" with suitable hedges. The suggestions in the question ("keeping with the sense", "in spirit", and "conceptually") don't feel right to me though, and seem somewhat of an oxymoron together with the word "quote". I would expect something like "loosely" or "roughly" e.g.

Loosely quoting Oscar Wilde, "truth isn't pure or simple"

Indirect speech is also generally assumed to be paraphrased, and often summarised e.g.

Oscar Wilde said that truth wasn't pure or simple

In especially informal contexts, quotative "like" indicates that speech is paraphrased, often with subtext drawn to the surface, and often for dramatic or humorous effect especially with a slightly exaggerated tone e.g.

Oscar Wilde was like, "that's rubbish, truth isn't pure or simple!"

There are also lots of phrases that can be used with direct speech to show that it's been paraphrased, but these generally only work with the verb "to say", and not "to quote" (which has the strong implication that the words that follow are verbatim). They can also often occur both immediately before or after the quote often with slight changes in the wording of the hedge e.g.

Oscar Wilde said, "truth isn't pure or simple", or words to that effect

Oscar Wilde said words to the effect of, "truth isn't pure or simple"

As others have said, "to paraphrase" is perfectly apt. An alternative with a slightly broader meaning is "to borrow", as in:

Borrowing from Seneca, luck is a function of preparation and opportunity.